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BEGIN:VEVENT
SUMMARY:Konrad Aguilar (University of Southern Denmark)
DTSTART:20200422T190000Z
DTEND:20200422T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/1
DESCRIPTION:Title: Quantum metrics on the tensor product of a commutative C*-algebra a
nd an AF C*-algebra.\nby Konrad Aguilar (University of Southern Denmar
k) as part of Noncommutative geometry in NYC\n\n\nAbstract\nGiven a compac
t metric space X and a unital AF algebra A equipped with a faithful tracia
l state\, we place quantum\nmetrics on the tensor product of C(X) and A gi
ven established quantum metrics on C(X) and A from work with Bice\nand Lat
remoliere. We prove the inductive limit of C(X) tensor A given by A is a m
etric limit in the Gromov-Hausdorff\npropinquity. We show that our quantum
metric is compatible with the tensor product by producing a Leibniz rule
on\nelementary tensors and showing the diameter of our quantum metric on t
he tensor product is bounded above the diameter\nof the Cartesian product
of the quantum metric spaces. We provide continuous families of C(X) tenso
r A which extends\nour previous results with Latremoliere on UHF algebras.
\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicola Ciccoli (Università di Perugia)
DTSTART:20200506T190000Z
DTEND:20200506T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/2
DESCRIPTION:Title: Orbit correspondence and groupoid C*-algebras\nby Nicola Ciccol
i (Università di Perugia) as part of Noncommutative geometry in NYC\n\n\n
Abstract\nIn those NC C*-algebras arising as quantization of a Poisson man
ifold one can try to establish a relation between the symplectic foliation
of the manifold and the unitary dual of its quantization. This relation i
s what goes under the name of orbit correspondence. In the best behaved ca
ses this correspondence is an homeomorphism. We will review some results o
n specific examples\, stressing the use of "groupoid quantization" as a t
ool to better understand features of this correspondence.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jim Tao 🇳🇴 (Norwegian University of Science and Technology)
DTSTART:20200429T190000Z
DTEND:20200429T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/3
DESCRIPTION:Title: A twisted local index formula for curved noncommutative two tori\nby Jim Tao 🇳🇴 (Norwegian University of Science and Technology) as
part of Noncommutative geometry in NYC\n\n\nAbstract\nWe consider the Dir
ac operator of a general metric in the \ncanonical conformal class on the
noncommutative two torus\, \ntwisted by an idempotent (representing the $K
$-theory class \nof a general noncommutative vector bundle)\, and derive a
local \nformula for the Fredholm index of the twisted Dirac operator. Our
\napproach is based on the McKean-Singer index formula\, and \nexplicit h
eat expansion calculations by making use of Connes' \npseudodifferential c
alculus. As a technical tool\, a new rearrangement \nlemma is proved to ha
ndle challenges posed by the noncommutativity of \nthe algebra and the pre
sence of an idempotent in the calculations in addition \nto a conformal fa
ctor. This is joint work with Farzad Fathizadeh and Franz Luef.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Branimir Cacic (University of New Brunswick)
DTSTART:20200513T190000Z
DTEND:20200513T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/4
DESCRIPTION:Title: Gauge theory on quantum principal bundles\nby Branimir Cacic (U
niversity of New Brunswick) as part of Noncommutative geometry in NYC\n\n\
nAbstract\nIn this talk\, I’ll give a brief (and somewhat idiosyncratic)
introduction to gauge theory on quantum principal bundles. I’ll give a
quick overview of the classical setting and sketch its noncommutative gene
ralisation à la Brzeziński–Majid\, Hajac\, et al. Then I’ll revisit
the notions of principal connection and gauge transformation from the pers
pective of recent work by Ć.–Mesland. I'll illustrate these concepts us
ing the irrational rotation algebra as a quantum principal U(1)-bundle ove
r the circle.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emil V Prodan (Yeshiva University)
DTSTART:20200603T190000Z
DTEND:20200603T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/5
DESCRIPTION:Title: Index theorems in KK-theory\nby Emil V Prodan (Yeshiva Universi
ty) as part of Noncommutative geometry in NYC\n\n\nAbstract\nConsider an e
xtended (Delone) point pattern in the d-dimensional Euclidean space such t
hat each point hosts N degrees of freedom. In many practical applications\
, ranging from quantum materials to meta-materials\, one is interested in
the collective dynamics of the degrees of freedom hosted by the pattern. A
s we shall see\, the generators of any pattern-equivariant dynamics belong
to a specific C*-algebra\, which in general takes the form of a groupoid
algebra and\, in more manageable cases\, of crossed products with discrete
groups. The non-commutative geometry program for the aperiodic patterns c
onsists in computing the C*-algebra\, its K-theory and cyclic co-homology\
, as well as establishing index theorems for the K-theory and cyclic co-ho
mology pairings. In these seminars I will describe several interesting cas
es where this program has been carried almost entirely. I have a large num
ber of numerical simulations\, which I will try to use throughout to exemp
lify the power of these methods.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emil V Prodan (Yeshiva University)
DTSTART:20200520T190000Z
DTEND:20200520T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/6
DESCRIPTION:Title: The C*-algebra of equivariant Hamiltonians over point patterns\
nby Emil V Prodan (Yeshiva University) as part of Noncommutative geometry
in NYC\n\n\nAbstract\nConsider an extended (Delone) point pattern in the d
-dimensional Euclidean space such that each point hosts N degrees of freed
om. In many practical applications\, ranging from quantum materials to met
a-materials\, one is interested in the collective dynamics of the degrees
of freedom hosted by the pattern. As we shall see\, the generators of any
pattern-equivariant dynamics belong to a specific C*-algebra\, which in ge
neral takes the form of a groupoid algebra and\, in more manageable cases\
, of crossed products with discrete groups. The non-commutative geometry p
rogram for the aperiodic patterns consists in computing the C*-algebra\, i
ts K-theory and cyclic co-homology\, as well as establishing index theorem
s for the K-theory and cyclic co-homology pairings. In these seminars I wi
ll describe several interesting cases where this program has been carried
almost entirely. I have a large number of numerical simulations\, which I
will try to use throughout to exemplify the power of these methods.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emil V Prodan (Yeshiva University)
DTSTART:20200527T190000Z
DTEND:20200527T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/7
DESCRIPTION:Title: Cyclic co-homology\, Fredholm modules\, Kasparov’s generalization
s\nby Emil V Prodan (Yeshiva University) as part of Noncommutative geo
metry in NYC\n\n\nAbstract\nConsider an extended (Delone) point pattern in
the d-dimensional Euclidean space such that each point hosts N degrees of
freedom. In many practical applications\, ranging from quantum materials
to meta-materials\, one is interested in the collective dynamics of the de
grees of freedom hosted by the pattern. As we shall see\, the generators o
f any pattern-equivariant dynamics belong to a specific C*-algebra\, which
in general takes the form of a groupoid algebra and\, in more manageable
cases\, of crossed products with discrete groups. The non-commutative geom
etry program for the aperiodic patterns consists in computing the C*-algeb
ra\, its K-theory and cyclic co-homology\, as well as establishing index t
heorems for the K-theory and cyclic co-homology pairings. In these seminar
s I will describe several interesting cases where this program has been ca
rried almost entirely. I have a large number of numerical simulations\, wh
ich I will try to use throughout to exemplify the power of these methods.\
n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Menevse Eryuzlu (Arizona State University)
DTSTART:20200610T190000Z
DTEND:20200610T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/8
DESCRIPTION:Title: Enchilada Categories\nby Menevse Eryuzlu (Arizona State Univers
ity) as part of Noncommutative geometry in NYC\n\n\nAbstract\nMuhly and So
lel developed a notion of Morita equivalence for C*-correspondences\, and
they \nproved a very important result: If two injective C*-correspondence
s are Morita equivalent then the corresponding Cuntz-Pimsner algebras are
Morita equivalent in the sense of Rieffel. \nInstead of proving it directl
y\, we build a functor that will give us the result of Muhly and Solel\, \
nin fact a more generalized version of their result\, as a special case.\
n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sara Azzali (Universität Hamburg)
DTSTART:20200617T190000Z
DTEND:20200617T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/9
DESCRIPTION:Title: KK-theory with real coefficients\, traces\, and discrete group acti
ons\nby Sara Azzali (Universität Hamburg) as part of Noncommutative g
eometry in NYC\n\n\nAbstract\nThe groups of KK-theory were introduced by K
asparov in the 1980’s and have important applications to many geometric
and topological problems which are tackled by C*-algebraic techniques. \n\
nIn this talk\, we investigate KK-theory groups with coefficients in $\\ma
thbb R$. By construction\, the adding of real coefficients provides natura
l receptacles for classes coming from traces on $C^*$-algebras. \nWe focus
on applications to the study of discrete groups actions on $C^*$-algebras
. \nWe show that in equivariant KK-theory with coefficients one can "local
ize at the unit element“ of the discrete group\, and this procedure has
interesting consequences on the Baum–Connes isomorphism conjecture.\nBas
ed on joint works with Paolo Antonini and Georges Skandalis.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jianchao Wu (Texas A & M)
DTSTART:20200624T190000Z
DTEND:20200624T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/10
DESCRIPTION:Title: The Novikov conjecture\, groups of diffeomorphisms\, and infinite
dimensional nonpositively curved spaces\nby Jianchao Wu (Texas A & M)
as part of Noncommutative geometry in NYC\n\n\nAbstract\nThe rational stro
ng Novikov conjecture is a prominent problem in noncommutative geometry. I
t implies deep conjectures in topology and differential geometry such as t
he (classical) Novikov conjecture on higher signatures and the Gromov-Laws
on conjecture on positive scalar curvature. Using C*-algebraic and K-theor
etic tools\, we prove that the rational strong Novikov conjecture holds fo
r geometrically discrete subgroups of the group of volume preserving diffe
omorphisms of any closed smooth manifold. The crucial geometric property o
f these groups that we exploit is the fact that they admit isometric and p
roper actions on a type of infinite-dimensional symmetric space of nonposi
tive curvature called the space of $L^2$-Riemannian metrics. In fact\, our
result holds for any discrete group admitting an isometric and proper act
ion on a (possibly infinite-dimensional) nonpositively curved space that w
e call an admissible Hilbert-Hadamard space\; thus our result partially ex
tends earlier ones of Kasparov and Higson-Kasparov. This is joint work wit
h Sherry Gong and Guoliang Yu.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chris Bruce (Queen Mary University of London)
DTSTART:20200708T190000Z
DTEND:20200708T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/11
DESCRIPTION:Title: C*-algebras from actions of congruence monoids\nby Chris Bruce
(Queen Mary University of London) as part of Noncommutative geometry in N
YC\n\n\nAbstract\nI will give an overview of recent results for semigroup
C*-algebras associated with number fields. These results are already inter
esting in the case where the field is the rational numbers\, and I will fo
cus mostly on this case to make everything more explicit and accessible.\n
C*-algebras of full ax+b-semigroups over rings of algebraic integers were
first studied by Cuntz\, Deninger\, and Laca\; their construction has sinc
e been generalized by considering actions of congruence monoids. Semigroup
C*-algebras obtained this way provide an example class of unital\, separa
ble\, nuclear\, strongly purely infinite C*-algebras which\, in many cases
\, completely characterize the initial number-theoretic data. They also ca
rry canonical time evolutions\, and the associated C*-dynamical systems ex
hibit intriguing phenomena. For instance\, the striking similarity between
the K-theory formula and the parameterization space for the low temperatu
re KMS states\, observed by Cuntz in the case of the full ax+b-semigroup\,
persists in the more general setting.\nPart of this work is joint with Xi
n Li\, and part is joint with Marcelo Laca and Takuya Takeishi.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Raphael Ponge (Sichuan University)
DTSTART:20200715T190000Z
DTEND:20200715T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/12
DESCRIPTION:Title: Analysis on curved noncommutative tori\nby Raphael Ponge (Sich
uan University) as part of Noncommutative geometry in NYC\n\n\nAbstract\nN
oncommutative tori are important examples of noncommutative spaces. Follow
ing seminal work by Connes-Tretkoff\, Connes-Moscovici\, Fathizadeh-Khalkh
ali\, and others a differential geometric apparatus on NC tori is currentl
y being built. So far the main focus has been mostly on conformal deformat
ion of the (flat) Euclidean metric or product of such metrics. \n\nThis ta
lk will report on ongoing work to deal with general Riemannian metrics on
NC tori (in the sense of Jonathan Rosenberg). Results include local and mi
crolocal Weyl laws\, Gauss-Bonnet theorems metrics\, and local index form
ulas.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tushar Das (University of Wisconsin - La Crosse)
DTSTART:20200805T190000Z
DTEND:20200805T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/13
DESCRIPTION:Title: The Varieties of Discrete Experience\, and Other Tales of Isometri
c Actions on Gromov Hyperbolic Metric Spaces\nby Tushar Das (Universit
y of Wisconsin - La Crosse) as part of Noncommutative geometry in NYC\n\n\
nAbstract\nWe survey joint work with David Simmons and Mariusz Urbanski th
at explores extensions of the classical theory of Kleinian groups acting o
n a finite-dimensional hyperbolic space to analogous actions on hyperbolic
metric spaces in the sense of Gromov\, a broad class of spaces which incl
udes infinite-dimensional rank one symmetric spaces of noncompact type and
much more!\n\nSeveral phenomena induced by greater degrees of freedom tha
n in finite dimensions (e.g. the different shades of discreteness alluded
to in the title) introduce new delicacies and thereby uncover fresh seams
that await investigation. The talk is aimed at students and beginners who
are unencumbered by the wisdom of experts and others tragically burdened b
y knowing too much. Being a novice\, any help from the audience in generat
ing new questions will be graciously accepted.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anna Duwenig (University of Wollongong)
DTSTART:20200701T190000Z
DTEND:20200701T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/14
DESCRIPTION:Title: Non-commutative Poincaré Duality of the irrational rotation algeb
ra\nby Anna Duwenig (University of Wollongong) as part of Noncommutati
ve geometry in NYC\n\n\nAbstract\nThe irrational rotation algebra is known
to be self-dual in a KK-theoretic sense. The required K-homology fundamen
tal class was constructed by Connes out of the Dolbeault operator on the 2
-torus\, but there has not been an explicit description of the dual elemen
t. In this talk\, I will geometrically construct that K-theory class by us
ing a pair of transverse Kronecker flows on the 2-torus. This is based on
joint work with my PhD advisor\, Heath Emerson.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Haluk Sengun (University of Sheffield)
DTSTART:20200722T190000Z
DTEND:20200722T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/15
DESCRIPTION:Title: Selberg's Trace Formula in operator K-theory\nby Haluk Sengun
(University of Sheffield) as part of Noncommutative geometry in NYC\n\n\nA
bstract\nSelberg introduced his celebrated trace formula in 1956. Since\nt
hen\, the trace formula has become an indispensable tool in number\ntheory
\, with spectacular applications to the Langlands program. After an\nexpos
ition of the trace formula\, I will present an identity in the\nsetting of
K-theory of group C*-algebras that is an analogue of the\ntrace formula.
Time remaining\, I will exhibit how one can derive the\nindex theoretic ve
rsion of the trace formula (due to Barbasch and\nMoscovici) from our ident
ity via the theory of higher indices.\n\nThis is joint work with Bram Mesl
and (Leiden) and Hang Wang (Shanghai).\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jerry Kaminker (UC Davis)
DTSTART:20200729T190000Z
DTEND:20200729T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/16
DESCRIPTION:Title: Odd analytic differential K-homology\nby Jerry Kaminker (UC Da
vis) as part of Noncommutative geometry in NYC\n\n\nAbstract\nDifferential
K-theory can be viewed as K-theory for vector bundles with connection. We
are\ndeveloping a dual version in the the Brown-Douglas-Fillmore setting
of K-homology. The\nrole of a connection is played by a projection. Our go
al is to obtain secondary invariants for\npairs of projections that yield
equivalent Toeplitz extensions. The talk will include a general discussion
of differential K-theory. This is joint work with Xiang Tang.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:John Quigg (Arizona State University)
DTSTART:20200819T190000Z
DTEND:20200819T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/17
DESCRIPTION:Title: Baum-Connes\, coactions\, and the Tilde Problem\nby John Quigg
(Arizona State University) as part of Noncommutative geometry in NYC\n\n\
nAbstract\nTrouble with the Baum-Connes Conjecture (with coefficients) can
in some way be blamed upon the existence of groups for which the reduced-
crossed-product functor is not exact. The full crossed product is exact bu
t doesn't fix the conjecture. Efforts to fix the conjecture have focused u
pon the ``minimal exact crossed product''\, whose existence is known throu
gh abstract nonsense\, but a construction remains elusive. Baum\, Guentner
\, and Willett propose a candidate formed in part by tensoring with a fixe
d action. Our contribution to the [BGW] ``exotic crossed product'' program
involves composing the full crossed product with coaction functors\, hopi
ng that the shift to coactions will add new insights. In particular\, we r
eplace the [BGW] candidate by tensoring with a fixed coaction. For a long
time we had a hard time proving that our functor is exact. The ``natural''
approach involves embedding into ``tilde multiplier algebras'' (which I'l
l define in the talk). But we can't see how to prove that this gives an ex
act functor\, and we call this the Tilde Problem. To get around this\, we
initially proved exactness of our coaction functor another --- extremely u
nsatisfying --- way: a long odyssey through equivariant C*-correspondences
\, ``natural'' Morita equivalence\, crossed-product duality\, and --- the
final humiliation --- appealing to exactness of the [BGW] crossed-product
functor itself\, completely thwarting our goal of doing everything within
the realm of coactions. Fortunately\, we recently saw how to use our incom
plete knowledge of the tilde functor to prove exactness of our coaction fu
nctor.\nThis is joint work with Steve Kaliszewski and Magnus Landstad.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robin Deeley (University of Colorado\, Boulder)
DTSTART:20200812T190000Z
DTEND:20200812T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/18
DESCRIPTION:Title: Minimal dynamical systems with prescribed K-theory\nby Robin D
eeley (University of Colorado\, Boulder) as part of Noncommutative geometr
y in NYC\n\n\nAbstract\nI will speak about joint work in progress with Ian
Putnam and Karen Strung. The goal of the project is to study the existenc
e of minimal homeomorphisms on compact metric spaces. In particular\, I wi
ll discuss partial results related to the following question: What is the
range of the K-theory (or more generally the Elliott invariant) for minima
l crossed products? Our approach to this question is based on the systemat
ic construction of minimal homeomorphisms with prescribed K-theoretic prop
erties.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anton Yu. Savin (Peoples' Friendship University\, Moscow)
DTSTART:20200826T190000Z
DTEND:20200826T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/19
DESCRIPTION:Title: A local index formula for metaplectic operators\nby Anton Yu.
Savin (Peoples' Friendship University\, Moscow) as part of Noncommutative
geometry in NYC\n\n\nAbstract\nLet A be the algebra of unitary operators a
cting in $H=L_2(R^n)$ and generated by translations\, orthogonal transform
ations\, products with exponentials $e^{ikx}$\nand fractional Fourier tran
sforms. Equivalently\, A is the algebra generated by quantizations of isom
etric affine canonical transformations in $T^*R^n$. We show that the well-
known index one operator in $R^n$ (which is obtained from the creation and
annihilation operators\, see Higson-Kasparov-Trout 1998) denoted by D def
ines a spectral triple (A\,H\,D) in the sense of Connes. Our main result i
s an explicit formula for the Connes--Moscovici residue cocycle for this s
pectral triple. For the subalgebra in A generated by translations and exp
onentials\, this gives a local index formula for noncommutative tori. \nTh
is is joint work with Elmar Schrohe (Hannover)\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pierre Clare (William & Mary)
DTSTART:20201007T190000Z
DTEND:20201007T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/20
DESCRIPTION:Title: Essential representations of real reductive groups\nby Pierre
Clare (William & Mary) as part of Noncommutative geometry in NYC\n\n\nAbst
ract\nThe tempered dual of a real reductive group G equipped with the Fell
\ntopology identifies with the space of irreducible representations of the
\nreduced C*-algebra of G. The Connes-Kasparov isomorphism allows to\ncomp
ute the K-theory of this C*-algebra by using the index theory of\nDirac-ty
pe operators on the symmetric space G/K. The goal of the work\npresented h
ere (joint with N. Higson\, Y. Song and X. Tang) is to provide\na represen
tation-theoretic approach to this isomorphism. We will\ndescribe the struc
ture of the reduced C*-algebra up to Morita\nequivalence and characterize
representations that contribute to the\nK-theory in terms of Dirac cohomol
ogy.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mahya Ghandehari (University of Delaware)
DTSTART:20200916T190000Z
DTEND:20200916T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/21
DESCRIPTION:Title: Fourier algebras of the group of $\\mathbb{R}$-affine transformati
ons and a dual convolution\nby Mahya Ghandehari (University of Delawar
e) as part of Noncommutative geometry in NYC\n\n\nAbstract\nA major trend
in Non-commutative Harmonic Analysis is to investigate function spaces rel
ated to Fourier analysis (and representation theory) of non-abelian groups
.\n\nThe Fourier algebra\, which is associated with the left regular repre
sentation of the ambient group\, is an important example of such function
spaces. This function algebra encodes the properties of the group in vario
us ways\; for instance the existence of derivations on this algebra transl
ates into information about the commutativity of the group itself. \n\n\n\
nIn this talk\, we investigate the Fourier algebra of the group of $\\math
bb{R}$-affine transformations. In particular\, we discuss the non-commuta
tive Fourier transform for this group\, and provide an explicit formula f
or the convolution product on the ``dual side'' of this transform. As an a
pplication of this new dual convolution product\, we show an easy dual for
mulation for (the only known) symmetric derivative on the Fourier algebra
of the group. \n\n\n\nThis talk is mainly based on joint articles with Y.
Choi.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Toke Meier Carlsen (University of the Faroe Islands)
DTSTART:20200902T190000Z
DTEND:20200902T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/22
DESCRIPTION:Title: Cuntz-Krieger algebras\, topological Markov shifts and groupoids\nby Toke Meier Carlsen (University of the Faroe Islands) as part of Non
commutative geometry in NYC\n\n\nAbstract\nIt is well-known that there is
a strong connection between Cuntz-Krieger algebras and a certain type of s
hifts of finite type called topological Markov shifts. Recently\, it has b
een discovered that topological Markov shifts can be recovered up to diffe
rent kinds of equivalence from the corresponding Cuntz-Krieger algebras.\n
\nI will give an overview of these results and explain how groupoids can b
e used to prove and generalise them.\n\nThe talk will primarily be based o
n the following papers.\n\nK. Matsumoto: "Orbit equivalence of topological
Markov shifts and Cuntz-Krieger algebras".\n\nK. Matsumoto: "Continuous o
rbit equivalence\, flow equivalence of Markov shifts and circle actions on
Cuntz–Krieger algebras".\n\nK. Matsumoto and H. Matui: "Continuous orbi
t equivalence of topological Markov shifts and Cuntz–Krieger algebras".\
n\nT. M. Carlsen\, S. Eilers\, E. Ortega\, and G. Restorff: "Flow equivale
nce and orbit equivalence for shifts of finite type and isomorphism of the
ir groupoids".\n\nT. M. Carlsen and J. Rout: "Diagonal-preserving gauge-in
variant isomorphisms of\ngraph C*-algebras".\n\nT. M. Carlsen\, E. Ruiz\,
A. Sims\, and M. Tomforde: "Reconstruction of groupoids and C*-rigidity of
dynamical systems".\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrey Glubokov (Ave Maria University\, Florida)
DTSTART:20200909T190000Z
DTEND:20200909T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/23
DESCRIPTION:Title: Cluster Algebras and their applications to Index Theorem\nby A
ndrey Glubokov (Ave Maria University\, Florida) as part of Noncommutative
geometry in NYC\n\n\nAbstract\nCluster Algebras were introduced in 2000 by
Fomin and Zelevinsky and since then their applications were developed in
many areas of mathematics and theoretical physics. We would like to introd
uce some of the Cluster Algebras and to explore the connections between th
em and Jones Index Theorem.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sayan Chakraborty (Indian Statistical Institute\, Kolkata)
DTSTART:20200923T190000Z
DTEND:20200923T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/24
DESCRIPTION:Title: Morita equivalence of noncommutative orbifolds\nby Sayan Chakr
aborty (Indian Statistical Institute\, Kolkata) as part of Noncommutative
geometry in NYC\n\n\nAbstract\nWe consider group actions on noncommutative
tori and study the corresponding 'noncommutative quotients' as crossed pr
oduct C*-algebras. We will show how such actions appear naturally and also
give Morita equivalence classes of such crossed products. The results are
an extension of similar results obtained by Elliott and Rieffiel for the
case of noncommutative tori.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cristian Ivanescu (MacEwan University\, Alberta)
DTSTART:20200930T190000Z
DTEND:20200930T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/25
DESCRIPTION:Title: The Cuntz semigroup and the classification of separable amenable C
*-algebras\nby Cristian Ivanescu (MacEwan University\, Alberta) as par
t of Noncommutative geometry in NYC\n\n\nAbstract\nNuclear C*-algebras (or
equivalently amenable C*-algebras) are a large class of C*-algebras amena
ble to study due to their finite-dimensional approximation property. Z-sta
ble C*-algebras are C*-algebras that satisfy a regularity property which p
roves fundamental for the known classification results that we know so far
. In this talk\, I will describe the Cuntz semigroup and its properties. E
vidence that the Cuntz semigroup can be used as an invariant to classify a
menable C*-algebras will be discussed.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maxim Braverman (Northeastern University)
DTSTART:20201014T190000Z
DTEND:20201014T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/26
DESCRIPTION:Title: Spectral Flow of Toeplitz operators and bulk-edge correspondence\nby Maxim Braverman (Northeastern University) as part of Noncommutative
geometry in NYC\n\n\nAbstract\nWe show that the (graded) spectral flow of
a family of Toeplitz operators on a complete Riemannian manifold is equal
to the index of a certain Callias-type operator. When the dimension of th
e manifold is even this leads to a cohomological formula for the spectral
flow. As an application\, we compute the spectral flow of a family of Toep
litz operators on a strongly pseudoconvex domain in $\\mathbb{C}^n$. This
result is similar to the Boutet de Monvel's computation of the index of a
single Toeplitz operator on a strongly pseudoconvex domain. Finally\, we s
how that the bulk-boundary correspondence in a tight-binding model of topo
logical insulators is a special case of our results. At the end I will exp
lain KK-theoretical extension of the main theaorem to families of Toeplitz
operators parametrized by an arbitrary compact manifold\, obtained by Koe
n van den Dungen.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andre Kornell (Tulane University)
DTSTART:20201118T200000Z
DTEND:20201118T210000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/27
DESCRIPTION:Title: Finite quantum structures\nby Andre Kornell (Tulane University
) as part of Noncommutative geometry in NYC\n\n\nAbstract\nWeaver's quantu
m relations provide a basis for a unified understanding of several classes
of quantum structures. In full generality\, quantum relations are defined
for arbitrary von Neumann algebras\, but to simplify the discussion\, thi
s talk will focus on finite-dimensional von Neumann algebras. I will talk
about quantum graphs\, quantum posets\, quantum groups\, quantum metric sp
aces and quantum families of permutations and of graph isomorphisms. I wil
l emphasize that each of these quantum generalizations can be motivated fr
om Birkhoff and von Neumann's original conception of quantum logic as the
logic of closed subspaces of a Hilbert space. (arXiv:2004.04377)\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gabor Etesi (Budapest University of Technology and Economics)
DTSTART:20201021T190000Z
DTEND:20201021T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/28
DESCRIPTION:Title: The universal von Neumann algebra of smooth 4-manifolds with an ap
plication to gravity\nby Gabor Etesi (Budapest University of Technolog
y and Economics) as part of Noncommutative geometry in NYC\n\n\nAbstract\n
Making use of its smooth structure only\, out of a connected\noriented smo
oth $4$-manifold a von Neumann algebra is constructed. As a\nspecial four
dimensional phenomenon this von Neumann algebra is\napproximated by algebr
aic (i.e.\, formal) curvature tensors of the\nunderlying $4$-manifold and
the von Neumann algebra itself is a\nhyperfinite factor of ${\\rm II}_1$ t
ype hence is unique up to abstract\nisomorphisms of von Neumann algebras.
Nevertheless over a fixed\n$4$-manifold this von Neumann algebra admits a
representation on a Hilbert\nspace such that its unitary equivalence class
is preserved by\norientation-preserving diffeomorphisms. Consequently the
Murray--von\nNeumann coupling constant of this representation is well-def
ined and gives\nrise to a new and computable real-valued smooth $4$-manifo
ld invariant: In\nan appropriate sense this invariant along all simply con
nected closed\n$4$-manifolds is generated by its surely non-trivial value
on\n${\\mathbb C}P^2$ (with its standard smooth structure) alone.\n\nIn th
e second half of the seminar (i.e. if time remains) some consequences\nof
this construction for quantum gravity are also discussed. Namely\nreversin
g the construction by starting not with a particular smooth\n$4$-manifold
but with the unique hyperfinite ${\\rm II}_1$ factor\, a\nconceptually sim
ple but manifestly four dimensional\, covariant\,\nnon-perturbative and ge
nuinely quantum theory is introduced whose\nclassical limit is general rel
ativity in an appropriate sense. Therefore\nit is reasonable to consider i
t as a sort of quantum theory of gravity. In\nthis model\, among other int
eresting things\, the observed positive but\nsmall value of the cosmologic
al constant acquires a natural explanation.\n\nReference\n\n1. G. Etesi: T
he universal von Neumann algebra of smooth four-manifolds\,\nto appear in
Adv. Theor. Math. Phys.\, arXiv: 1712.01828 [math-ph]\;\n\n2. G. Etesi: Gr
avity as a four dimensional algebraic quantum field theory\,\nAdv. Theor.
Math. Phys. 20\, 1049-1082 (2016)\, arXiv: 1402.5658 [hep-th].\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Valentin Deaconu (University of Nevada\, Reno)
DTSTART:20201028T190000Z
DTEND:20201028T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/29
DESCRIPTION:Title: Symmetries of the $C^∗$-algebra of a vector bundle\nby Valen
tin Deaconu (University of Nevada\, Reno) as part of Noncommutative geomet
ry in NYC\n\n\nAbstract\nWe consider $C^*$-algebras constructed from compa
ct group actions on complex vector bundles $E\\to X$ endowed with a Hermi
tian metric. An action of $G$ by isometries on $E\\to X$ induces an act
ion on the $C^*$-correspondence $\\Gamma(E)$ over $C(X)$ consisting of c
ontinuous sections\, and on the associated Cuntz-Pimsner algebra $\\mathca
l{O}_E$\, so we can study the crossed product $\\mathcal{O}_E\\rtimes G$.\
n\nIf the action is free and rank $E=n$\, then we prove that $\\mathcal{O
}_E\\rtimes G$ is \nMorita-Rieffel equivalent to a field of Cuntz algebras
$\\mathcal O_n$ over the orbit space $X/G$.\n\nIf the action is fiberwi
se\, then $\\mathcal{O}_E\\rtimes G$ becomes a continuous field of crossed
products $\\mathcal{O}_n\\rtimes G$. For transitive actions\, we show th
at \n$\\mathcal{O}_E\\rtimes G$ is Morita-Rieffel equivalent to a graph $C
^*$-algebra.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Erik van Erp (Dartmouth College)
DTSTART:20201104T200000Z
DTEND:20201104T210000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/30
DESCRIPTION:Title: The Heisenberg calculus\, index theory\, and cyclic cohomology
\nby Erik van Erp (Dartmouth College) as part of Noncommutative geometry i
n NYC\n\n\nAbstract\nOn a compact contact manifold\, a pseudodifferential
operator with an invertible symbol in the Heisenberg calculus is a hypoell
iptic Fredholm operator. Its symbol determines an element in the K-theory
of the noncommutative algebra of Heisenberg symbols. In joint work with Al
exander Gorokhovksy\, we construct a cyclic cocycle which\, when paired wi
th the Connes-Chern character of the principal Heisenberg symbol\, calcula
tes the index.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nik Weaver (Washington University)
DTSTART:20201111T200000Z
DTEND:20201111T210000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/31
DESCRIPTION:Title: Quantum graph theory\nby Nik Weaver (Washington University) as
part of Noncommutative geometry in NYC\n\n\nAbstract\nIn recent years ope
rator systems --- unital self-adjoint spaces of operators --- have come to
be seen as "quantum" graphs. The original motivation for this analogy ca
me from quantum error correction\, but the subject has developed a life of
its own. I will discuss quantum Ramsey theory\, the quantum Turan proble
m\, and quantum chromatic number.\n\nI will mostly stick to the finite dim
ensional setting\, so there will be few prerequisites beyond linear algebr
a over the complex numbers.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bram Mesland (Leiden University)
DTSTART:20201125T200000Z
DTEND:20201125T210000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/32
DESCRIPTION:Title: Gabor frames and Wannier bases from groupoid Morita equivalences\nby Bram Mesland (Leiden University) as part of Noncommutative geometry
in NYC\n\n\nAbstract\nA key question in Gabor analysis is the reconstruct
ion of elements in a Hilbert space \nvia a Gabor frame. Gabor frames arise
from a finite set of vectors acted upon by a canonically defined \nset of
operators (typically translation and modulation). \nThis data is often co
nveniently encoded in the algebraic structure of a groupoid. In this talk
we will discuss how the natural notion of Morita equivalence of groupoids
gives rise to Gabor frames for the Hilbert space localisation of \nthe Mor
ita equivalence bimodule of the reduced groupoid $C^*$-algebras. For finit
ely generated and projective submodules\, we show these Gabor frames are o
rthonormal \nbases if and only if the module is free. \nIf time allows\, w
e will discuss an application of this result to spectral subspaces of Schr
oedinger operators with atomic potentials supported on (aperiodic) Delone
sets.\n\nThis is joint work with Chris Bourne (Tohoku University)\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Jekel (UC San Diego)
DTSTART:20201202T200000Z
DTEND:20201202T210000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/33
DESCRIPTION:Title: Non-commutative transport of measure\nby David Jekel (UC San D
iego) as part of Noncommutative geometry in NYC\n\n\nAbstract\nGiven self-
adjoint operators $X_1\, \\dots\, X_d$ and $Y_1\, \\dots\, Y_d$\, it is di
fficult to tell when the von Neumann algebra generated by the $X_j$'s and
$Y_j$'s are isomorphic. Viewing the operators as non-commutative random v
ariables\, the isomorphism of von Neumann algebras is equivalent to the ex
istence of a non-commutative function that will push forward the non-commu
tative probability distribution of $X = (X_1\,\\dots\,X_d)$ to that of $Y
=(Y_1\,\\dots\,Y_d)$. It was proved by Guionnet\, Shlyakhtenko\, and Dabr
owski that certain nice non-commutative probability distributions known as
free Gibbs laws can be transported to the non-commutative Gaussian distri
bution\, and thus the associated von Neumann algebras are all isomorphic.
More recently\, we have shown that this transport can be done in a lower
triangular manner\, so that the von Neumann algebra generated by $X_1\, \\
dots\, X_k$ is mapped to the von Neumann algebra generated by $Y_1\, \\dot
s\, Y_k$ for $k = 1\, \\dots\, d$. Furthermore\, this transport arises in
a natural way as the large-$n$ limit of classical transport of measure fo
r random variables in the space of $d$-tuples $n \\times n$ matrices that
approximate $(X_1\,\\dots\,X_d)$ as $n \\to \\infty$.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Goncalo Tabuada (University of Warwick)
DTSTART:20210120T160000Z
DTEND:20210120T170000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/34
DESCRIPTION:Title: Noncommutative Weil conjecture\nby Goncalo Tabuada (University
of Warwick) as part of Noncommutative geometry in NYC\n\n\nAbstract\nThe
Weil conjectures (proved by Deligne in the 70's) played a key role in the
development of modern algebraic geometry. In this talk I will extend the W
eil conjectures from the realm of algebraic geometry to the broad noncommu
tative setting of differential graded categories and describe some of its
numerous applications.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthew Kennedy (University of Waterloo)
DTSTART:20210127T200000Z
DTEND:20210127T210000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/35
DESCRIPTION:Title: Amenability\, proximality and higher order syndeticity\nby Mat
thew Kennedy (University of Waterloo) as part of Noncommutative geometry i
n NYC\n\n\nAbstract\nI will present new descriptions of some universal flo
ws associated to a discrete group\, obtained using what we view as a kind
of "topological Furstenberg correspondence." The descriptions are algebra
ic and relatively concrete\, involving subsets of the group satisfying a h
igher order notion of syndeticity. We utilize them to establish new necess
ary and sufficient conditions for strong amenability and amenability. Furt
hermore\, utilizing similar techniques\, we obtain a characterization of "
dense orbit sets\," answering a question of Glasner\, Tsankov\, Weiss and
Zucker. Throughout the talk\, I will discuss connections to operator algeb
ras.\n\nThis is joint work with Sven Raum and Guy Salomon.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vrej Zarikian (U.S. Naval Academy)
DTSTART:20210203T200000Z
DTEND:20210203T210000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/36
DESCRIPTION:Title: Unique Extension Properties for C*-Inclusions\nby Vrej Zarikia
n (U.S. Naval Academy) as part of Noncommutative geometry in NYC\n\n\nAbst
ract\nLet $\\mathcal{A} \\subseteq \\mathcal{B}$ be a $C^*$-inclusion\, i.
e.\, an inclusion of unital $C^*$-algebras with the same unit. Structural
properties of the inclusion are often reflected by the fact that certain f
amilies of UCP (unital completely positive) maps on $\\mathcal{A}$ extend
uniquely to UCP maps on $\\mathcal{B}$. In particular\, depending on the s
tructure of $\\mathcal{A} \\subseteq \\mathcal{B}$\, it could be the case
that\n\ni. every pure state on $\\mathcal{A}$ extends uniquely to a pure s
tate on $\\mathcal{B}$ (i.e.\, $\\mathcal{A} \\subseteq \\mathcal{B}$ has
the pure extension property)\;\n\nii. a weak* dense set of pure states on
$\\mathcal{A}$ extend uniquely to pure states on $\\mathcal{B}$ (i.e.\, $\
\mathcal{A} \\subseteq \\mathcal{B}$ has the almost extension property)\;\
n\niii. the identity map $\\operatorname{id}:\\mathcal{A} \\to \\mathcal{A
}$ extends uniquely to a UCP map $E:\\mathcal{B} \\to \\mathcal{A}$ (i.e.\
, $\\mathcal{A} \\subseteq \\mathcal{B}$ has a unique conditional expectat
ion)\;\n\niv. the identity map $\\operatorname{id}:\\mathcal{A} \\to \\mat
hcal{A}$ extends uniquely to a UCP map $\\theta:\\mathcal{B} \\to I(\\math
cal{A})$\, where $I(\\mathcal{A})$ is the injective envelope of $\\mathcal
{A}$ (i.e.\, $\\mathcal{A} \\subseteq \\mathcal{B}$ has a unique pseudo-ex
pectation).\n\nIn this talk\, we explore properties (i)-(iv) above\, with
a special emphasis on abelian inclusions $C(X) \\subseteq C(Y)$ and inclus
ions $\\mathcal{A} \\subseteq \\mathcal{A} \\rtimes_r G$ arising from acti
ons of discrete groups. Applications to determining the simplicity of redu
ced crossed products are provided.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Francesca Arici (Leiden University)
DTSTART:20201209T200000Z
DTEND:20201209T210000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/37
DESCRIPTION:Title: SU(2)-symmetries\, exact sequences of C*-algebras and subproduct s
ystems\nby Francesca Arici (Leiden University) as part of Noncommutati
ve geometry in NYC\n\n\nAbstract\nMotivated by the study of symmetries of
C*-algebras as well as by multivariate operator theory\, in this talk we w
ill introduce the notion of an SU(2)-equivariant subproduct system of Hilb
erts spaces. Through an explicit construction in operator theory\, we will
obtain Toeplitz and Cuntz-Pimsner algebras\, and provide results about t
heir topological invariants. \n\nIn particular\, we will show that the Toe
plitz algebra of the subproduct system of an irreducible SU(2) representat
ion is equivariantly KK-equivalent to the algebra of complex numbers\, so
that the (K)K-theory groups of the Cuntz-Pimsner algebra can be effectivel
y computed using an exact sequence involving an analogue of the Euler clas
s.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marat Markin (California State University\, Fresno)
DTSTART:20201216T200000Z
DTEND:20201216T210000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/38
DESCRIPTION:Title: On the Smoothness of Weak Solutions of an Abstract Evolution Equat
ion with a Scalar Type Spectral Operator\nby Marat Markin (California
State University\, Fresno) as part of Noncommutative geometry in NYC\n\n\n
Abstract\nGiven the abstract evolution equation\n\n$$y\\prime (t) = Ay(t)\
, \\quad t ≥ 0\, \\hskip2cm (AEE)$$\n\nwith a scalar type spectral opera
tor $A$ in a complex Banach space\, we find conditions on $A$\, formulated
exclusively in terms of the location of its spectrum in the complex plane
\, necessary and sufficient for all weak solutions of the equation\, which
a priori need not be strongly differentiable\, to be strongly infinite di
fferentiable or strongly Gevrey ultradifferentiable of order $\\beta\\ge 1
$\, \nin particular analytic or entire\, on $[0\,\\infty)$ or \n$(0\, \\in
fty)$. We also reveal certain inherent smoothness improvement effects and
show that\, if all weak solutions of the equation are Gevrey ultradifferen
tiable of orders less than one\, then the operator is necessarily bounded.
\n\nIn addition\, we find characterizations of the generation of strongly
infinite differentiable and Gevrey ultradifferentiable $C_0$-semigroups by
scalar type spectral operators.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sylvie Paycha (Universität Potsdam)
DTSTART:20210210T200000Z
DTEND:20210210T210000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/39
DESCRIPTION:Title: Regularised traces and Getzler’s rescaling revisited\nby Syl
vie Paycha (Universität Potsdam) as part of Noncommutative geometry in NY
C\n\n\nAbstract\nInspired by Gilkey's invariance theory\, Connes' deforma
tion to the\nnormal cone and Getzler's rescaling method\, we single out a
class of\ngeometric operators among pseudodifferential operators acting on
\nsections of a class of natural vector bundles\, to which we attach a \nr
escaling degree.\nThis degree is then used to express regularised traces
of geometric\noperators in terms of a rescaled limit of Wodzicki residue
s. When\napplied to complex powers of the square of a Dirac operator\, thi
s \namounts to expressing the index of a Dirac operator in terms of a loca
l\nresidue involving the Getzler rescaled limit of its square.\n\nThis
is joint work with Georges Habib.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Clément Dell'Aiera (ENS Lyon)
DTSTART:20210217T200000Z
DTEND:20210217T210000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/40
DESCRIPTION:Title: Dynamic asymptotic dimension and homology\nby Clément Dell'Ai
era (ENS Lyon) as part of Noncommutative geometry in NYC\n\n\nAbstract\nGr
oupoid homology has attracted increasing attention from from the topologic
al dynamics and operator algebras communities following the work of Matui.
Matui's HK conjecture predicts that the K-theory groups of the reduced C*
-algebra of a minimal essentially principal ample groupoid coincides with
its homology groups. We prove that homology of principal ample groupoids v
anish in degree above its dynamical asymptotic dimension\, a notion of dim
ension from topological dynamics. We deduce several consequences: Matui's
HK conjecture holds for low dimensional principal ample groupoids\, and cl
assification of their reduced C*-algebra. (Joint work with Christian Bonic
ke\, Jamie Gabe and Rufus Willett)\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aristides Katavolos (University of Athens)
DTSTART:20210224T200000Z
DTEND:20210224T210000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/41
DESCRIPTION:Title: Harmonic functions\, crossed products and approximation properties
\nby Aristides Katavolos (University of Athens) as part of Noncommutat
ive geometry in NYC\n\n\nAbstract\nThe space of harmonic functions on a lo
cally compact group $G$ is the fixed point space of a\ncertain Markov oper
ator. Its `quantization'\, the corresponding fixed point space of operator
s on $L^2(G)$\, coincides with the weak-* closed bimodule over the group v
on Neumann algebra generated by this space. We examine the analogous space
s of jointly harmonic functions\nand their quantized operator bimodules. T
his leads to two different notions of crossed product of operator spaces b
y actions of $G$\, which coincide when $G$ satisfies a certain approximati
on property. The corresponding (dual) notions of crossed products of (co-)
actions by the von Neumann algebra of $G$ always coincide. This gives a n
ew approach to the correspondence between spectral synthesis and operator
synthesis.\n\n\nThe talk is a survey of joint work with M. Anoussis and I.
G. Todorov\, and of recent work by D. Andreou.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Gonçalves (Universidade Federal de Santa Catarina)
DTSTART:20210303T200000Z
DTEND:20210303T210000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/42
DESCRIPTION:Title: A generalization of shifts of finite type motivated by C*-algebra
theory\nby Daniel Gonçalves (Universidade Federal de Santa Catarina)
as part of Noncommutative geometry in NYC\n\n\nAbstract\nUltragraphs algeb
ras generalized Exel-Laca and graph algebras. In this talk we describe ult
ragraphs\, their associated edge shift spaces (which generalize SFT for in
finite alphabets)\, and their associated C*-algebras and groupoids. At the
end\, we present results regarding continuous orbit equivalence and full
groups associated to ultragraphs\, and describe how to apply these results
to graph and Exel-Laca algebras.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joakim Arnlind (Linköping University)
DTSTART:20210310T200000Z
DTEND:20210310T210000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/43
DESCRIPTION:Title: Curvature for a class of noncommutative minimal surfaces\nby J
oakim Arnlind (Linköping University) as part of Noncommutative geometry i
n NYC\n\n\nAbstract\nThe theory of minimal surfaces is an old and still qu
ite active field\nof research\, and it is natural to ask if there exists a
corresponding\ntheory in noncommutative geometry? In particular\, analogu
es of minimal\nsubmanifolds appear in physical theories related to quantum
gravity\n(string/membrane theory). I will present an approach to noncommu
tative\nminimal surfaces taking an equational point of view (rather than a
\nvariational one). After providing some background material leading to\no
ur definition of noncommutative minimal surfaces\, I will discuss a\nframe
work for constructing Levi-Civita connections and curvature of\nsuch surfa
ces. These considerations naturally lead to a general\ndiscussion of metri
c connections on hermitian modules.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cédric Arhancet (Lycée Lapérouse)
DTSTART:20210317T190000Z
DTEND:20210317T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/44
DESCRIPTION:Title: Entangling quantum information theory and Fourier multipliers on o
perator algebras\nby Cédric Arhancet (Lycée Lapérouse) as part of N
oncommutative geometry in NYC\n\n\nAbstract\nOne of the most fundamental q
uestions in quantum information concerns with the amount of information th
at can be transmitted reliably through a quantum channel. For that\, many
capacities and entropies was introduced for describing the capability of t
he channel for delivering information from the sender to the receiver. In
this talk\, we will explain how to obtain the exact values of some of thes
e quantities for large classes of channels by using the theory of Fourier
multipliers on quantum groups.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yulia Kuznetsova (Université de Franche-Comté)
DTSTART:20210324T190000Z
DTEND:20210324T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/45
DESCRIPTION:Title: Quantum semigroups\, what is known or not\nby Yulia Kuznetsova
(Université de Franche-Comté) as part of Noncommutative geometry in NYC
\n\n\nAbstract\nWhereas it is straightforward to define a topological grou
p\, one\nneeds more caution when dealing with semigroups: their multiplica
tion might\nbe only separately and not jointly continuous. This happens in
the case as\nnatural as the weakly almost periodic of a locally compact g
roup. The\ndistinction exists also in the quantum case\, first addressed b
y Mattthew\nDaws. After discussing it\, I will speak on duality and known
links with\nquantum compactifications. Finally\, I will pass to some resul
ts on the\nstructure of quantum semigroups. The last part is work in progr
ess with\nBiswarup Das.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor Fulman (Arizona State University)
DTSTART:20210428T190000Z
DTEND:20210428T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/47
DESCRIPTION:Title: Introduction to von Neumann Algebras\, I\nby Igor Fulman (Ariz
ona State University) as part of Noncommutative geometry in NYC\n\n\nAbstr
act\nBasic examples. Strong\, weak and operator norm topology. Bicommutant
theorem.\nProjections.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor Fulman (Arizona State University)
DTSTART:20210505T190000Z
DTEND:20210505T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/48
DESCRIPTION:Title: Introduction to von Neumann Algebras\, II\nby Igor Fulman (Ari
zona State University) as part of Noncommutative geometry in NYC\n\n\nAbst
ract\nFactors. Direct sum of factors. Finite and infinite projections. Pur
ely infinite projections. Factors of type I\, II and III. Examples.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor Fulman (Arizona State University)
DTSTART:20210512T190000Z
DTEND:20210512T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/49
DESCRIPTION:Title: Introduction to von Neumann Algebras\, III\nby Igor Fulman (Ar
izona State University) as part of Noncommutative geometry in NYC\n\n\nAbs
tract\nExamples of factors of type I\, II and III . Group von Neumann alge
bras. Crossed products.\nIntroduction to Tomita-Takesaki theory.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vasilisa Shramchenko (Université de Sherbrooke)
DTSTART:20210421T190000Z
DTEND:20210421T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/50
DESCRIPTION:Title: Poncelet theorem and Painlevé VI\nby Vasilisa Shramchenko (Un
iversité de Sherbrooke) as part of Noncommutative geometry in NYC\n\n\nAb
stract\nIn 1995 Hitchin constructed explicit algebraic solutions to the Pa
inlevé VI (1/8\,-1/8\,1/8\,3/8) equation starting with any Poncelet traj
ectory\, that is a closed billiard trajectory inscribed in a conic and cir
cumscribed about another conic. In this talk I will show that Hitchin's co
nstruction is nothing but the Okamoto transformation between Picard's solu
tion and the general solution of the Painlevé VI (1/8\,-1/8\,1/8\,3/8) eq
uation. Moreover\, this Okamoto transformation can be written in terms of
an Abelian differential of the third kind on the associated elliptic curve
.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor Nikolaev (St. John's University)
DTSTART:20210331T190000Z
DTEND:20210331T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/51
DESCRIPTION:Title: Quantum dynamics of elliptic curves\nby Igor Nikolaev (St. Joh
n's University) as part of Noncommutative geometry in NYC\n\n\nAbstract\nW
e calculate the $K$-theory of a crossed product $C^*$-algebra \n $\\mat
hscr{A}_{RM}\\rtimes\\mathscr{E}(K)$\, where $\\mathscr{A}_{RM}$ is the
\n noncommutative torus with real multiplication and $\\mathscr{E}(K)$ i
s an elliptic curve \n over the number field $K$. We use this result to
evaluate the rank and \n the Shafarevich-Tate group of $\\mathscr{E}(K)
$.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Angel Roman (William & Mary)
DTSTART:20210407T190000Z
DTEND:20210407T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/52
DESCRIPTION:Title: The Mackey bijection for reductive groups and continuous fields of
reduced group C*-algebras\nby Angel Roman (William & Mary) as part of
Noncommutative geometry in NYC\n\n\nAbstract\nIn the 1970's\, George Mack
ey proposed that there should be some kind of analogy between unitary repr
esentations of semisimple groups $G$ and unitary representations of its C
artan motion group $G_0=K\\ltimes \\mathfrak{g}/\\mathfrak{k}$\, where $K$
is a maximal compact subgroup of $G$. Eventually a precise bijection was
constructed between the irreducible tempered unitary representations of $G
$ and the irreducible unitary representations of $G_0$. In a joint work wi
th Nigel Higson we characterized the Mackey bijection using continuous fie
lds of reduced group $C^*$-algebra of complex reductive group. We construc
ted an embedding between the reduced $C^*$-algebras of $G_0$ and $G$. Time
permitting\, I will discuss ongoing work (with Nigel Higson and Pierre Cl
are) toward a generalization to a wider class of groups.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Frei (University of Copenhagen)
DTSTART:20210414T190000Z
DTEND:20210414T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/53
DESCRIPTION:Title: Relative Cuntz-Pimsner algebras: Gauge-invariant uniqueness theore
m and the lattice of gauge-invariant ideals\nby Alexander Frei (Univer
sity of Copenhagen) as part of Noncommutative geometry in NYC\n\n\nAbstrac
t\nWe start with an abstract definition of C*-correspondences comparing th
em to Fell bundles.\nAfter a first few basic results\, we then swiftly mov
e on to their representations.\nWe introduce here the concept of covarianc
es and relative Cuntz-Pimsner algebras.\n\nFrom here we go into a detailed
analysis of covariances within the category of C*-correpondences.\nWe obt
ain here a systematic reduction leading us to a parametrisation of relativ
e Cuntz-Pimsner algebras.\n\nWith this at hand we arrive at the gauge-inva
riant uniqueness theorem\, for all (arbitrary) gauge-equivariant represent
ations at once.\n\nFrom here we move on to the analysis part of the progra
m.\nWe study the covariances in the case of the Fock representation and it
s quotients.\nAs a result we derive that the parametrisation of relative C
untz-Pimsner algebras is classifying.\nIn other words\, we obtain a comple
te and intrinsic picture of the lattice of quotients\, and equivalently of
gauge-invariant ideals.\n\nIf time permits\, we finish off with the next
chapter on their induced Fell bundles\, as already investigated by Schweiz
er.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Katz (St. John's University)
DTSTART:20210602T190000Z
DTEND:20210602T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/54
DESCRIPTION:Title: On real Sigma*-algebras\nby Alexander Katz (St. John's Univers
ity) as part of Noncommutative geometry in NYC\n\n\nAbstract\nReal analogu
es of (complex) Sigma*-algebras are introduced and their basic properties
and connections with real von Neumann algebras are discussed.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexandre Afgoustidis (CNRS\, l’Institut Élie Cartan de Lorrain
e)
DTSTART:20210519T150000Z
DTEND:20210519T160000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/55
DESCRIPTION:Title: The tempered dual of real or p-adic reductive groups\, and its non
commutative geometry (joint work with Anne-Marie Aubert)\nby Alexandre
Afgoustidis (CNRS\, l’Institut Élie Cartan de Lorraine) as part of Non
commutative geometry in NYC\n\n\nAbstract\nSuppose G is a real or p-adic r
eductive group. The space of irreducible tempered representations of G com
es equipped with the Fell topology\, which encodes important phenomena in
representation theory. The topology is usefully studied by noncommutative
-geometric methods: the tempered dual naturally identifies with the spectr
um of the C*-algebra of G\, and its connected components identify with the
spectra of certain `blocks’ in the C*-algebra. \n\nFor real reductive g
roups\, A. Wassermann proved in 1987 that each `block’ has\, up to Morit
a equivalence\, a beautiful and simple structure. This was a crucial step
in his proof of the Baum-Connes-Kasparov conjecture for G. For p-adic grou
ps\, it is not obvious at all that such a structure can exist\, but import
ant examples were given by R. Plymen and his students. \n\nIn my talk\, I
will report on joint work with Anne-Marie Aubert which (1) for arbitrary G
\, gives a geometric condition for the existence of a Wassermann-type stru
cture on a given block\, and (2) when G is a quasi-split symplectic\, orth
ogonal or unitary group\, explicitly determines the connected components o
f the tempered dual for which the geometric assumption is satisfied.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christian Bonicke (University of Glasgow)
DTSTART:20210526T190000Z
DTEND:20210526T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/56
DESCRIPTION:Title: Regularity properties for ample groupoids and the type semigroup\nby Christian Bonicke (University of Glasgow) as part of Noncommutative
geometry in NYC\n\n\nAbstract\nI will introduce the type semigroup of an
ample groupoid and explain how it encodes dynamical properties of the grou
poid in an algebraic framework. In particular I will explain how the fine
structure of the type semigroup relates to certain regularity properties o
f the groupoid\, which play a prominent role in recent attempts to develop
a dynamical analogue of the Toms-Winter conjecture for simple separable n
uclear C*-algebras.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Francesc Perera (Universitat Autònoma de Barcelona)
DTSTART:20210609T190000Z
DTEND:20210609T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/57
DESCRIPTION:Title: Traces on ultrapower C*-algebras\nby Francesc Perera (Universi
tat Autònoma de Barcelona) as part of Noncommutative geometry in NYC\n\n\
nAbstract\nEvery sequence of traces on a C*-algebra induces a limit trace
on a free ultrapower. I will discuss the natural question of characterizin
g when this set of limit traces is dense\, and mention the use of techniqu
es coming from the theory of Cuntz semigroups to obtain such a characteriz
ation. This talk is based on joint work with Ramon Antoine\, Leonel Robert
\, and Hannes Thiel.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shanna Dobson (California State University\, Los Angeles)
DTSTART:20210623T190000Z
DTEND:20210623T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/58
DESCRIPTION:Title: Pro-Diamond and the Geometrization of Local Langlands\nby Shan
na Dobson (California State University\, Los Angeles) as part of Noncommut
ative geometry in NYC\n\n\nAbstract\nWe recently conjectured a pro-diamond
in our Efimov K-theory of Diamonds\, for diamonds in the sense of Scholze
. In this talk\, we discuss our pro-diamond formalism and survey the many
incarnations of diamonds in the geometrization of the local Langlands Corr
espondence.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anne-Marie Aubert (CNRS\, Sorbonne Université - Université de Pa
ris)
DTSTART:20210630T190000Z
DTEND:20210630T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/59
DESCRIPTION:Title: Stratified equivalences and Bernstein Center\nby Anne-Marie Au
bert (CNRS\, Sorbonne Université - Université de Paris) as part of Nonco
mmutative geometry in NYC\n\n\nAbstract\nIn the first part of the talk\, w
e will introduce the notion of stratified equivalence for finite type k-al
gebras\, which is a weakening of Morita equivalence\, and illustrate it wi
th examples.\n\nNext\, we will recall the Bernstein decomposition of the c
ategory of smooth representations of a p-adic reductive group and show how
stratified equivalence occurs in this context\, notably in the case of in
ner forms of the special linear group.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fabio Cipriani (Politecnico di Milano)
DTSTART:20210714T190000Z
DTEND:20210714T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/60
DESCRIPTION:Title: On a noncommutative Sierpiński gasket\nby Fabio Cipriani (Pol
itecnico di Milano) as part of Noncommutative geometry in NYC\n\n\nAbstrac
t\nWe illustrate the construction of a C*-algebra A that can be genuinely
interpreted as a quantization of the classical Sierpiński gasket\, the mo
st studied instance of a self-similar fractal space. We further describe t
he discrete and continuous spectrum of A\, the structure of the traces on
A as well as the construction of a Dirichlet form E and of a spectral trip
le (A\,D\,H).\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/60/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pieter Spaas (UCLA)
DTSTART:20210707T190000Z
DTEND:20210707T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/61
DESCRIPTION:Title: Cohomological obstructions to lifting properties for full C*-algeb
ras of property (T) groups\nby Pieter Spaas (UCLA) as part of Noncommu
tative geometry in NYC\n\n\nAbstract\nWe will introduce and discuss the li
fting property (LP) and local lifting property (LLP) for full group C*-alg
ebras. We will then introduce a new method to refute these properties\, ba
sed on non-vanishing of second cohomology groups. This will allow us to de
rive that many natural examples of (relative) property (T) groups fail the
LLP\, and further large classes fail the LP. This is based on joint work
with Adrian Ioana and Matthew Wiersma.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/61/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mitch Haslehurst (University of Victoria)
DTSTART:20210616T190000Z
DTEND:20210616T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/62
DESCRIPTION:Title: Relative K-theory with applications to factor groupoids\nby Mi
tch Haslehurst (University of Victoria) as part of Noncommutative geometry
in NYC\n\n\nAbstract\nIn this talk I will speak about a portrait of relat
ive K-theory for C*-algebras inspired by a setup due to Max Karoubi using
Banach categories. After presenting some useful exact sequences\, I will s
how how the portrait gives the same data\, although through a different le
ns\, as the K-groups that arise from the mapping cone construction. After
this\, I will \npresent some examples of C*-algebras from factor groupoids
whose K-theory data are computable (in fact\, controllable\, to a certain
degree) using these relative K-theory tools.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jens Kaad (University of Southern Denmark)
DTSTART:20210818T190000Z
DTEND:20210818T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/63
DESCRIPTION:Title: Exterior products of compact quantum metric spaces\nby Jens Ka
ad (University of Southern Denmark) as part of Noncommutative geometry in
NYC\n\n\nAbstract\nThe theory of compact quantum metric spaces was initiat
ed by Rieffel in the late nineties. Important inspiration came from the fu
ndamental observation of Connes saying that the metric on a compact spin m
anifold can be recovered from the Dirac operator. A compact quantum metric
space is an operator system (e.g. a unital C*-algebra) equipped with a se
minorm which metrizes the weak-*-topology on the state space via the assoc
iated Monge-Kantorovich metric. In this talk we study tensor products of c
ompact quantum metric spaces with specific focus on seminorms arising from
the exterior product of spectral triples. On our way we obtain a novel ch
aracterization of compact quantum metric spaces using finite dimensional a
pproximations and we apply this characterization to propose a completely b
ounded version of the theory.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/63/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Scott Schmieding (University of Denver)
DTSTART:20210721T190000Z
DTEND:20210721T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/64
DESCRIPTION:Title: Flow equivalence and mapping class groups for symbolic dynamical s
ystems\nby Scott Schmieding (University of Denver) as part of Noncommu
tative geometry in NYC\n\n\nAbstract\nThere have been many fruitful connec
tions between symbolic dynamical systems and operator algebras. We'll firs
t give a very brief survey of some examples of this\, before focusing on t
he notion of flow equivalence and mapping class groups in the context of s
ymbolic dynamics. The talk will be designed so that little to no knowledge
of dynamical systems is necessary.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/64/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bernhard Burgstaller (Universidade Federal de Santa Catarina)
DTSTART:20210728T190000Z
DTEND:20210728T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/65
DESCRIPTION:Title: A kind of KK-theory of rings\nby Bernhard Burgstaller (Univers
idade Federal de Santa Catarina) as part of Noncommutative geometry in NYC
\n\n\nAbstract\nA group equivariant $KK$-theory\nfor rings will be defined
and studied\nin analogy to Kasparov's $KK$-theory for\n$C^*$-algebras.\nI
t is a kind of linearization of the category\nof rings by allowing additio
n of homomorphisms\, imposing also homotopy invariance\, invertibility of
matrix corner embeddings\,\nand allowing morphisms which are the opposite
split of split exact sequences.\nWe demonstrate the potential of this theo
ry\nby proving for example equivalence induced by Morita equivalence\nand
a Green-Julg isomorphism in this framework.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/65/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Laurent Cantier (Universitat Autònoma de Barcelona)
DTSTART:20210908T190000Z
DTEND:20210908T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/66
DESCRIPTION:Title: Classification of unitary elements of a C*-algebra\nby Laurent
Cantier (Universitat Autònoma de Barcelona) as part of Noncommutative ge
ometry in NYC\n\n\nAbstract\nThe Cuntz semigroup has emerged as an essenti
al tool for the classification of (non-simple) C*-algebras. For instance\,
it has been shown that the functor Cu classifies positive elements of any
C*-algebra of stable rank 1 (up to approximately unitarily equivalence).
An immediate corollary is that the Cuntz semigroup is a complete invariant
for AI algebras. In this talk\, I will raise the question of classificati
on of unitary elements of a C*-algebra (of stable rank 1). It is unlikely
that the Cuntz semigroup alone is sufficient to classify these elements an
d one can speculate that an ingredient with $K_1$ flavor has to be added.
Nevertheless\, I will prove that this remains true when restricting to AF
algebras and I will discuss how one could to extend this classification re
sult to a larger class of C*-algebra.\n\nEven though I will recall definit
ions of the Cuntz semigroup and classifying functor\, it might good to poi
nt out that knowledge about C*-algebras are needed.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/66/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lyudmila Turowska (Chalmers University of Technology)
DTSTART:20210901T190000Z
DTEND:20210901T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/67
DESCRIPTION:Title: Multipliers and Approximation Properties\nby Lyudmila Turowska
(Chalmers University of Technology) as part of Noncommutative geometry in
NYC\n\n\nAbstract\nOne can encode various properties of locally compact g
roups from properties of Banach algebras associated to the groups and vice
versa. In this talk I will explain how Herz-Schur multipliers have been u
sed to study some of those properties. Then I will talk about generalizati
on of such multipliers to the setting of dynamical systems and explain how
the technique of Herz-Schur multipliers can be extended to study approxim
ation properties of crossed product C*-algebras. I shall also discuss comp
act and completely compact multipliers.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/67/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stefan Wagner (Blekinge Institute of Technology)
DTSTART:20210825T190000Z
DTEND:20210825T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/68
DESCRIPTION:Title: Factor systems as a computational framework for noncommutative pri
ncipal bundles - with an application to Atiyah’s famous Lie algebra sequ
ence\nby Stefan Wagner (Blekinge Institute of Technology) as part of N
oncommutative geometry in NYC\n\n\nAbstract\nFree C*-dynamical systems\, i
n the sense of Ellwood\, provide a natural framework for noncommutative pr
incipal bundles\, which are becoming increasingly prevalent in various app
lications to noncommutative geometry and mathematical physics. \nOne of th
e key features of free C*-dynamical systems are their associated factor sy
stems\, which make them accessible to classification\, K-theoretic conside
rations\, and computations in general. \nIn this talk we present the recen
t theory of factor systems for free C*-dynamical systems and apply it to g
ive a derivation-based Atiyah sequence for noncommutative principal bundle
s.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/68/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kevin Brix (University of Glasgow)
DTSTART:20210915T190000Z
DTEND:20210915T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/69
DESCRIPTION:Title: Flow equivalence and C*-algebras\nby Kevin Brix (University of
Glasgow) as part of Noncommutative geometry in NYC\n\n\nAbstract\nTopolog
ical dynamical systems are an abundant source of examples of interesting C
*-algebras\, e.g. Cuntz-Krieger algebras\, graph C*-algebras and their hig
her rank and twisted variations. Dynamical relations such as conjugacy or
flow equivalence are an invitation to study the fine structure of these C*
-algebras and isomorphisms between them. I intend to discuss some central
results as well as important open questions in this field.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/69/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Timothy Schenkel (Ohio University)
DTSTART:20210811T190000Z
DTEND:20210811T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/70
DESCRIPTION:Title: Regular Ideals of Locally-Convex Kumjian-Pask Algebras\nby Tim
othy Schenkel (Ohio University) as part of Noncommutative geometry in NYC\
n\n\nAbstract\nWe give a vertex set description for basic\, graded\, regul
ar ideals of locally-convex Kumjian-Pask Algebras. We also show that Condi
tion (B) is preserved when taking the quotient by a basic\, graded\, regul
ar ideal. We further show that when a locally-convex\, row-finite k-graph
satisfies Condition (B)\, all regular ideals are graded.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/70/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Diego Martínez (University of Madrid)
DTSTART:20211006T190000Z
DTEND:20211006T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/71
DESCRIPTION:Title: C* and geometric properties of inverse semigroups\nby Diego Ma
rtínez (University of Madrid) as part of Noncommutative geometry in NYC\n
\n\nAbstract\nInverse semigroups are a generalization of groups\, where el
ements in an inverse semigroup can be thought of as partial symmetries of
a space (instead of global symmetries\, as in the group case). Out of thes
e one can construct a uniform Roe algebra algebra just as in the group cas
e\, and study its properties. In this talk\, we shall characterize when su
ch C*-algebra is nuclear by means of an intrinsic metric in the semigroup\
, and prove that its nuclearity is equivalent to the semigroup having pro
perty A. Moreover\, one can also study amenability notions in this case\,
and relate the trace space of the uniform Roe algebra with certain invaria
nt measures in the semigroup. This talk is based on joint work with Pere A
ra and Fernando Lledó.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/71/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jorge Plazas (Pontificia Universidad Javeriana)
DTSTART:20210922T190000Z
DTEND:20210922T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/72
DESCRIPTION:Title: Noncommutative geometry of arithmetic groups\nby Jorge Plazas
(Pontificia Universidad Javeriana) as part of Noncommutative geometry in N
YC\n\n\nAbstract\nIn this talk we look at constructions from noncommutativ
e geometry which encode various number theoretic properties of arithmetic
groups.\n\nIn the first part of the talk we will discuss the relation betw
een Conway's big picture and the Connes-Marcolli Gl(2) system. This relati
on leads to noncommutative spaces encoding properties of groups commensur
able with the modular group. In the second part of the talk we discuss Hec
ke operators for Bianchi groups and the action of these in K-homology via
Bredon homology and the Baum-Connes conjecture.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/72/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tyrone Crisp (University of Maine)
DTSTART:20210929T190000Z
DTEND:20210929T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/73
DESCRIPTION:Title: Frobenius C*-algebras and local adjunctions of C*-correspondences<
/a>\nby Tyrone Crisp (University of Maine) as part of Noncommutative geome
try in NYC\n\n\nAbstract\nMany interesting and important C*-algebras do no
t have multiplicative identities\, and C*-algebraists have long known how
to deal with this fact by using approximate identities\, multiplier algebr
as\, etc. A similar situation arises when one attempts to use methods of c
ategory theory to study modules over C*-algebras: objects like "the catego
ry of compact operators on Hilbert spaces" don't fit neatly into the stand
ard theory of categories\, because they lack identity morphisms\; but they
do fit nicely into a theory of non-unital C*-categories and their multipl
ier categories\, as developed by Kandelaki\, Mitchener\, Vasselli\, Antoun
-Voigt\, and others. This talk concerns an adaptation of the important cat
egorical notion of adjoint functors to this non-unital-category point of v
iew. I will present a definition (taken from joint work with Pierre Clare
and Nigel Higson) of adjoint functors between categories of compact operat
ors on Hilbert C*-modules\, and I will explain how this definition corresp
onds to a natural notion of Frobenius C*-algebra\, mirroring a corresponde
nce between two-sided adjunctions and Frobenius algebras in classical cate
gory theory.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/73/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gilles Castro (Universidade Federal de Santa Catarina)
DTSTART:20211103T190000Z
DTEND:20211103T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/74
DESCRIPTION:Title: KMS states for generalized gauge actions on C*-algebras associated
with self-similar sets\nby Gilles Castro (Universidade Federal de San
ta Catarina) as part of Noncommutative geometry in NYC\n\n\nAbstract\nOn t
he one hand\, equilibrium states in quantum statistical mechanics can be d
escribed using the KMS condition. On the other hand\, in classical statist
ical mechanics\, one way of finding equilibrium states is via an operator
called the Ruelle operator. It turns out that for some noncommutative C*-a
lgebras built from classical objects\, there are some relationships betwee
n KMS states on the C*-algebras and properties of the Ruelle operator. In
this talk\, after recalling the needed definitions\, I will present some r
esults in this direction for C*-algebras associated with self-similar sets
.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/74/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Becky Armstrong (Universität Münster)
DTSTART:20211013T190000Z
DTEND:20211013T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/75
DESCRIPTION:Title: A uniqueness theorem for twisted groupoid C*-algebras\nby Beck
y Armstrong (Universität Münster) as part of Noncommutative geometry in
NYC\n\n\nAbstract\nTwisted groupoid C*-algebras were introduced by Renault
in 1980 and are a generalisation of twisted group C*-algebras\, which are
the C*-algebraic analogue of twisted group rings. Through the work of Ren
ault and more recently of Li\, it has emerged that every simple classifiab
le C*-algebra can be realised as a twisted groupoid C*-algebra\, a result
that has led to increased interest in the structure of these C*-algebras.
In this talk I will describe the construction of reduced twisted C*-algebr
as of Hausdorff étale groupoids. I will then discuss my recent preprint i
n which I prove a uniqueness theorem for these algebras and use this to ch
aracterise simplicity in the case where the groupoid is effective.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/75/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vadim Alekseev (Technische Universität Dresden)
DTSTART:20211110T200000Z
DTEND:20211110T210000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/76
DESCRIPTION:Title: Geometry of sofic approximations\nby Vadim Alekseev (Technisch
e Universität Dresden) as part of Noncommutative geometry in NYC\n\n\nAbs
tract\nIn the recent years\, there has been substantial activity\nconnecti
ng graph theory and group theory via the concept of a metric\napproximatio
n of an infinite group by finite objects (groups or\ngraphs)\, particularl
y around sofic groups. This lead to numerous\nresults which describe appro
ximation properties of the group (for\ninstance\, amenability or Haagerup
property) in terms of geometric\nproperties of its approximations (e.g. hy
perfiniteness or coarse\nembeddability in a Hilbert space of a graph seque
nce). In this talk\, I\nwill describe these connections between the two wo
rlds (groups and\ngraphs) and some recent results around them.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/76/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicolas Monod (École Polytechnique Fédérale de Lausanne)
DTSTART:20211020T190000Z
DTEND:20211020T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/77
DESCRIPTION:Title: Type I\, Gelfand pairs and Iwasawa decompositions\nby Nicolas
Monod (École Polytechnique Fédérale de Lausanne) as part of Noncommutat
ive geometry in NYC\n\n\nAbstract\nIn this talk\, we will prove that every
Gelfand pair admits an Iwasawa\ndecomposition.\n\nBefore that\, we will e
xplain what Gelfand pairs are and why Iwasawa\ndecompositions are useful.\
n\nAt the end\, we will discuss a conjecture studied in collaboration with
\nM. Kalantar and P.-E. Caprace\, speculating about similar results for\nt
ype I groups.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/77/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrey Glubokov (Purdue University)
DTSTART:20211027T190000Z
DTEND:20211027T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/78
DESCRIPTION:Title: Cluster algebra and Jones polynomials\nby Andrey Glubokov (Pur
due University) as part of Noncommutative geometry in NYC\n\n\nAbstract\nC
luster $C^*$-algebra of the sphere with two cusps and its K-theory is bein
g investigated to demonstrate a connection to the Jones polynomials.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/78/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aaron Tikuisis (University of Ottawa)
DTSTART:20211117T200000Z
DTEND:20211117T210000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/79
DESCRIPTION:Title: Nuclear dimension and Z-stability of simple C*-algebras\nby Aa
ron Tikuisis (University of Ottawa) as part of Noncommutative geometry in
NYC\n\n\nAbstract\nMuch recent work in C*-algebra theory has focused on re
gularity properties. This is a response to examples of "irregular" simple
nuclear C*-algebras by Villadsen (algebras with perforation in their order
ed K-theory)\, Rordam (algebras with both finite and infinite projections)
\, and Toms (algebras that cannot be distinguished by ordered K-theory and
traces). I will describe two regularity properties: finite nuclear dimens
ion and Z-stability (aka Jiang-Su-stability). In joint work with Castillej
os\, Evington\, White\, and Winter\, we showed that these properties coinc
ide for simple separable nuclear unital C*-algebras\, verifying a conjectu
re of Toms and Winter. I will discuss this result and its implications.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/79/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xin Ma (University of Memphis)
DTSTART:20211124T200000Z
DTEND:20211124T210000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/80
DESCRIPTION:Title: Fiberwise amenability and almost elementariness for étale groupoi
ds\nby Xin Ma (University of Memphis) as part of Noncommutative geomet
ry in NYC\n\n\nAbstract\nIn this talk\, I will discuss two new properties
for locally compact Hausdorff étale groupoids. One is from a coarse geome
tric view called fiberwise amenability. Another one is called almost eleme
ntariness\, which is a new finite-dimensional approximation property. I wi
ll explain how these notions related to almost finiteness defined by Matui
and refined by Kerr and show our almost elementariness implying tracial Z
-stability of reduced groupoid C*-algebras. As an application. This implie
s that Matui's almost finiteness in the groupoid setting also implies Z-st
ability when the groupoid is minimal 2nd countable and topological amenabl
e. This was open in general before. I will also present more applications
if time permits. This is based on joint work with Jianchao Wu.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/80/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yifeng Huang (University of Michigan)
DTSTART:20211201T200000Z
DTEND:20211201T210000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/81
DESCRIPTION:Title: Point count of the variety of modules over the quantum plane over
a finite field\nby Yifeng Huang (University of Michigan) as part of No
ncommutative geometry in NYC\n\n\nAbstract\nIn 1960\, Feit and Fine gave a
formula for the number of pairs of commuting n by n matrices over a finit
e field. We consider a quantum deformation of the problem\, namely\, count
ing pairs (A\,B) of n by n matrices over a finite field that satisfy AB=qB
A for a fixed nonzero scalar q. We give a formula for this count in terms
of the order of q as a root of unity\, generalizing Feit and Fine's result
. In this talk\, after explaining the title and the results\, we will disc
uss a curious phenomenon that one sees when comparing the commutative case
(q=1) and the general case from a geometric viewpoint.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/81/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Réamonn Ó Buachalla (Charles University\, Prague)
DTSTART:20211208T200000Z
DTEND:20211208T210000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/82
DESCRIPTION:Title: Quantum Root Vectors and a Dolbeault Double Complex for the A-Seri
es Quantum Flag Manifolds\nby Réamonn Ó Buachalla (Charles Universit
y\, Prague) as part of Noncommutative geometry in NYC\n\n\nAbstract\nIn th
e 2000s a series of seminal papers by Heckenberger and Kolb introduced an
essentially unique covariant $q$-deformed de Rham complex for the irreduci
ble quantum flag manifolds. In the years since\, it has become increasingl
y clear that these differential graded algebras have a central role to pla
y in the noncommutative geometry of Drinfeld–Jimbo quantum groups. Until
now\, however\, the question of how to extend Heckenberger and Kolb’s c
onstruction beyond the irreducible case has not been examined. Here we add
ress this question for the A-series Drinfeld–Jimbo quantum groups $U_q(\
\mathfrak{sl}_{n+1})$\, and show that for precisely two reduced decomposit
ions of the longest element of the Weyl group\, Lusztig’s associated spa
ce of quantum root vectors gives a quantum tangent space for the full quan
tum flag manifold $\\mathcal{O}_q(F_{n+1})$ with associated differential g
raded algebra of classical dimension. Moreover\, its restriction to the qu
antum Grassmannians recovers the $q$-deformed complex of Heckenberger and
Kolb\, giving a conceptual explanation for their origin. Time permitting\,
we will discuss the noncommutative Kähler geometry of these spaces and t
he proposed extension of the root space construction to the other series.
(Joint work with P. Somberg.)\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/82/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Priyanga Ganesan (Texas A&M)
DTSTART:20211215T200000Z
DTEND:20211215T210000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/83
DESCRIPTION:Title: Spectral bounds for chromatic number of quantum graphs\nby Pri
yanga Ganesan (Texas A&M) as part of Noncommutative geometry in NYC\n\n\nA
bstract\nQuantum graphs are a non-commutative generalization of classical
graphs that have appeared in different branches of mathematics including o
perator algebras\, non-commutative topology and quantum information theory
. In this talk\, I will review the different perspectives to quantum graph
s and introduce a chromatic number for quantum graphs using a non-local ga
me with quantum inputs and classical outputs. I will then show that many s
pectral lower bounds for chromatic numbers in the classical case (such as
Hoffman’s bound) also hold in the setting of quantum graphs. This is ach
ieved using an algebraic formulation of quantum graph coloring and tools f
rom linear algebra.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/83/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yavar Abdolmaleki (University of New Brunswick)
DTSTART:20220202T200000Z
DTEND:20220202T210000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/84
DESCRIPTION:Title: Equivariant KK-theory and its application in Index theory\nby
Yavar Abdolmaleki (University of New Brunswick) as part of Noncommutative
geometry in NYC\n\n\nAbstract\nIn this talk\, we show how using the calcul
ation of a couple of Kasparov products of asymptotically equivariant cycle
s we can find the index of an asymptotically equivariant Dirac-Schrodinger
operator on a Hyperbolic manifold. In fact\,\nusing the calculation of th
e Kasparov products of a couple of asymptotically equivariant cycles\, we
reduce the problem of finding the index to the\ncase in which the manifold
is compact and so the problem reduces to the Atiyah-Singer index theorem.
\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/84/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Federico Vigolo (University of Münster)
DTSTART:20220209T200000Z
DTEND:20220209T210000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/85
DESCRIPTION:Title: Strong ergodicity\, projections and Markov operators\nby Feder
ico Vigolo (University of Münster) as part of Noncommutative geometry in
NYC\n\n\nAbstract\nThe aim of this talk is to illustrate how some insights
from the theory of Markov processes can be adapted to prove that certain
projections belong to "Roe-like" C*-algebras of dynamical origin. Given an
action of a countable discrete group on a measure space\, one may define
a C*-algebra by taking the closure of an algebra of operators with finite
propagation. I will explain that this C*-algebra contains a certain natura
l family of rank-one projections if and only if the action is strongly erg
odic. This result can be used to construct more counterexamples to the coa
rse Baum-Connes conjecture.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/85/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ulrich Pennig (Cardiff University)
DTSTART:20220216T200000Z
DTEND:20220216T210000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/86
DESCRIPTION:Title: Bundles of C*-algebras - An Introduction to Dixmier-Douady theory<
/a>\nby Ulrich Pennig (Cardiff University) as part of Noncommutative geome
try in NYC\n\n\nAbstract\nA bundle of C*-algebras is a collection of algeb
ras continuously parametrised by a topological space. There are (at least)
two different definitions in operator algebras that make this intuition p
recise: Continuous C(X)-algebras provide a flexible analytic point of view
\, while locally trivial C*-algebra bundles allow a classification via hom
otopy theory. The section algebra of a bundle in the topological sense is
a C(X)-algebra\, but the converse is not true. In this talk I will compare
these two notions using the classical work of Dixmier and Douady on bundl
es with fibres isomorphic to the compacts as a guideline. I will then expl
ain joint work with Marius Dadarlat\, in which we showed that the theorems
of Dixmier and Douady can be generalized to bundles with fibers isomorphi
c to stabilized strongly self-absorbing C*-algebras. An important feature
of the theory is the appearance of higher analogues of the Dixmier-Douady
class.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/86/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Damien Rivet (Université Clermont Auvergne)
DTSTART:20220223T200000Z
DTEND:20220223T210000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/87
DESCRIPTION:Title: Geometric view of semisimple quantum groups representations\nb
y Damien Rivet (Université Clermont Auvergne) as part of Noncommutative
geometry in NYC\n\n\nAbstract\nThe representations of the principal series
of a semisimple quantum group can be\, as in the classical case\, constru
cted as induced representations from the characters of a quantum Borel sub
group. Rieffel's framework for induction can be adapted to quantum groups
and allows to give a simple expression for the principal series representa
tions. In particular this leads\, as Clare did in the classical case\, to
gather all these representations into a single Hilbert module built from a
certain quantum homogeneous space.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/87/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Makoto Yamashita (University of Oslo)
DTSTART:20220302T150000Z
DTEND:20220302T160000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/88
DESCRIPTION:Title: Homology and K-theory of dynamical systems\nby Makoto Yamashit
a (University of Oslo) as part of Noncommutative geometry in NYC\n\n\nAbst
ract\nA theory of homology for étale groupoids was developed by Crainic a
nd Moerdijk based on simplicial structure of nerves of groupoids\, as a co
mpanion to Haeflier's theory of cohomology for groupoids. We relate this t
o another (co)homology of groupoids\, namely the operator K-groups of the
associated convolution algebra\, when the base is totally disconnected. Su
ch a connection was conjectured by Matui through his study of Cantor dynam
ical systems. Our proof is based on the triangulated categorical structure
of groupoid equivariant KK-theory\, following the categorical approach to
the Baum-Connes conjecture by Meyer and Nest. Along the way we uncover th
e close connection to Putnam's homology theory for hyperbolic dynamical sy
stems (Smale spaces). Based on joint works with Valerio Proietti.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/88/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Francesco Fidaleo (Università di Roma "Tor Vergata")
DTSTART:20220314T150000Z
DTEND:20220314T160000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/89
DESCRIPTION:Title: Modular Spectral Triples and deformed Fredholm modules (Part I)\nby Francesco Fidaleo (Università di Roma "Tor Vergata") as part of Non
commutative geometry in NYC\n\n\nAbstract\nDue to possible applications to
the attempt to provide a set of equations which unify the four elementary
interactions in nature (the grand-unification) and in another\, perhaps c
onnected\, direction in proving the long-standing\, still unsolved\, Riema
nn conjecture about the zeroes of the $\\zeta$-function\, Connes’ non- c
ommutative geometry grew up rapidly in the last decades.\n\nAmong the main
objects introduced (by A. Connes) for handling noncommutative geometry th
ere are the so called spectral triples\, encoding most of the properties e
njoyed by the (quantum) ”manifold” into consideration\, and the associ
ated Fredholm modules.\n\nOn the other hand\, the so-called Tomita modular
theory is nowadays assuming an increasingly relevant role for several app
lications in mathematics and in physics. Such a scenario suggests the nece
ssary need to take the modular data into account in the investigation of q
uantum manifolds. In such a situation\, the involved Dirac operators shoul
d be suitably deformed (by the use of the modular operator)\, and should c
ome from non-type $II_1$ representations.\n\nTaking into account such comm
ents\, we discuss the preliminary necessary step consisting in the explici
t construction of examples of non type $II_1$ representations and relative
spectral triples\, called modular. This is done for the noncommutative 2-
torus $A_{\\alpha}$\, provided α is a (special kind of) Liouville number\
, where the nontrivial modular structure plays a crucial role.\n\nFor such
representations\, we briefly discuss the appropriate Fourier analysis\, b
y proving the analogous of many of the classical known theorems in harmoni
c analysis such as the Riemann-Lebesgue lemma\, the Hausdorff-Young theore
m\, and the $L_p$-convergence results associated to the Cesaro means (i.e.
the Fejer theorem) and the Abel means reproducing the Poisson kernel. We
show how those Fourier transforms ”diagonalise” appropriately some exa
mples of the Dirac operators associated to the previous mentioned spectral
triples.\n\nFinally\, we provide a definition of a deformed generalisatio
n of ”Fredholm module”\, i.e. a suitably deformed commutator of the
”phase” of the involved Dirac operator with elements of a subset (the
so-called Lipschitz $\\star$-algebra or Lipschitz operator system) which\,
depending on the cases under consideration\, is either a dense $\\star$-
algebra or an essential operator system. We also show that all models of m
odular spectral triples for the noncommutative 2-torus mentioned above enj
oy the property to being also a deformed Fredholm module. This definition
of deformed Fredholm module is new even in the usual cases associated to a
trace\, and could provide other\, hopefully interesting\, applications.\n
\nThe present talk is based on the following papers:\n\n[1] F. Fidaleo and
L. Suriano: Type $III$ representations and modular spectral triples for t
he noncommutative torus\, J. Funct. Anal. 275 (2018)\, 1484-1531.\n\n[2] F
. Fidaleo: Fourier analysis for type III representations of the noncommuta
tive torus\, J. Fourier Anal. Appl. 25 (201)\, 2801-2835.\n\n[3] F. Ciolli
and F. Fidaleo: Type $III$ modular spectral triples and deformed Fredholm
modules\, preprint.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/89/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Francesco Fidaleo (Università di Roma "Tor Vergata")
DTSTART:20220413T190000Z
DTEND:20220413T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/90
DESCRIPTION:Title: Spectral actions for q-particles and their asymptotic (Part II)\nby Francesco Fidaleo (Università di Roma "Tor Vergata") as part of Non
commutative geometry in NYC\n\n\nAbstract\nFor spectral actions made of th
e average number of particles and arising from open systems made of genera
l free $q$-particles (including Bose\, Fermi and classical ones correspond
ing to $q=\\pm1$ and $0$\, respectively) in thermal equilibrium\, we compu
te the asymptotic expansion with respect to the natural cut-off. We treat
both relevant situations relative to massless and massive particles\, wher
e the natural cut-off is $1/\\beta=k_{\\rm B}T$ and $1/\\sqrt{\\beta}$\, r
espectively. \nWe show that the massless situation enjoys less regularity
properties than the massive one. We also consider the passage to the cont
inuum describing infinitely extended open systems in thermal equilibrium.
We briefly discuss the appearance of condensation phenomena occurring for
Bose-like $q$-particles\, for which $q\\in(0\,1]$\, after passing to the c
ontinuum. We also compare the arising results for the finite volume situat
ion (discrete spectrum) with the corresponding infinite volume one (contin
uous spectrum).\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/90/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Edward McDonald (PennState)
DTSTART:20220323T190000Z
DTEND:20220323T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/91
DESCRIPTION:Title: Littlewood-Paley inequalities and other analytic issues in noncomm
utative Euclidean spaces\nby Edward McDonald (PennState) as part of No
ncommutative geometry in NYC\n\n\nAbstract\nI will discuss some analytic i
ssues that arose in the course of investigations of the problem of charact
erising quantum differentiability in noncommutative spaces. These issues h
ighlight some of the peculiar features of certain noncommutative spaces wh
ere classical results become meaningless or trivially false. In particular
I discuss the apparent lack of a Poincaré inequality on noncommutative E
uclidean planes (Moyal planes) and how this necessitates the use of new te
chniques.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/91/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Raphael Ponge (Sichuan University)
DTSTART:20220330T190000Z
DTEND:20220330T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/92
DESCRIPTION:Title: Dixmier trace formulas and negative eigenvalues of Schroedinger op
erators on noncommutative tori\nby Raphael Ponge (Sichuan University)
as part of Noncommutative geometry in NYC\n\n\nAbstract\nIn this talk\, we
shall first address a question raised by Alain Connes during a conference
at Fudan University in Shanghai in 2017. We will also explain a link that
has come to light only recently between noncommutative geometry and the w
ork of Birman-Solomyak on semiclassical analysis of Schroedinger operators
in the 70s. We will then present results obtained jointly with Ed McDonal
d (UNSW-Sydney) on Cwikel-type estimates on NC tori. As an application we
obtain a version of Connes' integration formulas under very weak assumptio
ns. Further applications include versions of the Cwikel-Lieb-Rozenblum an
d Lieb-Thirring inequalities for negative eigenvalues of Schroedinger oper
ators on noncommutative tori. Ultimately\, we get a seminclassical Weyl la
w for curved noncommutative tori\, i.e.\, NC tori endowed with arbitrary R
iemannian metrics.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/92/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oleg Yu. Aristov (Moscow State University)
DTSTART:20220406T140000Z
DTEND:20220406T150000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/93
DESCRIPTION:Title: Complex analytic quantum groups\nby Oleg Yu. Aristov (Moscow S
tate University) as part of Noncommutative geometry in NYC\n\n\nAbstract\n
We discuss a missing link in quantum group theory - quantum analogues of c
omplex Lie groups. As such analogues\, I propose to take topological Hopf
algebras with a finiteness condition (holomorphically finitely generated
or HFG for short). This approach is not directly related to C*-algebraic q
uantum groups (at least for now) but is an alternative view. Nevertheless
\, the topic seems to offer a wide range of research opportunities.\n\nOur
focus is on examples\, such as analytic forms of some classical quantum g
roups (a deformation of a solvable Lie group and Drinfeld-Jimbo algebras)
. I also present some general results: 1) the category of Stein groups is
anti-equivalent to the category of commutative Hopf HFG algebras\; 2) If
$G$ is a compactly generated Lie group\, the cocommutative topological H
opf algebra $\\widehat{A(G)}$ (naturally associated with $G$) is HFG. W
hen in addition\, $G$ is connected linear\, the structure of $\\widehat{A
(G)}$ can be described explicitly.\n\nI also plan to discuss briefly holom
orphic duality in the sense of Akbarov (which is parallel to Pontryagin du
ality).\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/93/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Karen Strung (Czech Academy of Sciences)
DTSTART:20220504T190000Z
DTEND:20220504T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/94
DESCRIPTION:Title: An introduction to C*-algebras\, I\nby Karen Strung (Czech Aca
demy of Sciences) as part of Noncommutative geometry in NYC\n\n\nAbstract\
nBanach algebras\, definition of C*-algebra\, spectrum\, Gelfand transform
\, characters.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/94/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Karen Strung (Czech Academy of Sciences)
DTSTART:20220511T190000Z
DTEND:20220511T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/95
DESCRIPTION:Title: An introduction to C*-algebras\, II\nby Karen Strung (Czech Ac
ademy of Sciences) as part of Noncommutative geometry in NYC\n\nAbstract:
TBA\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/95/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Benton Duncan (North Dakota State University)
DTSTART:20220907T190000Z
DTEND:20220907T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/96
DESCRIPTION:Title: Abstract operator algebras and enveloping C*-algebras\nby Bent
on Duncan (North Dakota State University) as part of Noncommutative geomet
ry in NYC\n\n\nAbstract\nWe will consider nonselfadjoint operator algebras
and the $C^*$-algebras they generate. We will look at motivating examples
of classes of nonselfadjoint operator algebras. We will outline several c
onstructions of enveloping $C^*$-algebras for operator algebras and develo
p examples of the various enveloping $C^*$-algebras.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/96/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mariusz Tobolski (University of Wrocław)
DTSTART:20220420T190000Z
DTEND:20220420T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/97
DESCRIPTION:Title: Noncommutative numerable principal bundles from group actions on C
*-algebras\nby Mariusz Tobolski (University of Wrocław) as part of No
ncommutative geometry in NYC\n\n\nAbstract\nThe notion of a compact noncom
mutative (or quantum) principal bundle\, which generalizes the Cartan comp
act principal bundle from topology (local triviality not assumed)\, emerge
d in the literature almost 30 years ago. Recently\, the difficulty of intr
oducing the local-triviality condition to the noncommutative realm was ove
rcome using the notion of the local-triviality dimension of an action of a
compact quantum group on a unital C*-algebra. In this talk\, I will propo
se a definition of a locally trivial noncommutative principal bundle in th
e setting of actions of locally compact Hausdorff groups on (possibly non-
unital) C*-algebras. I will discuss various motivations and technical diff
iculties that appear in the non-compact case. I will also provide some bas
ic results and examples. The key difference is that\, although the problem
itself can be described in the language of C*-algebra\, one is quickly le
d beyond the Gelfand-Naimark duality and to the theory of multipliers of t
he Pedersen ideal.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/97/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Karen Strung (Czech Academy of Sciences)
DTSTART:20220525T190000Z
DTEND:20220525T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/99
DESCRIPTION:Title: An introduction to C*-algebras\, III\nby Karen Strung (Czech A
cademy of Sciences) as part of Noncommutative geometry in NYC\n\nAbstract:
TBA\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/99/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Slawomir Klimek (Indiana University–Purdue University Indianapol
is)
DTSTART:20220427T190000Z
DTEND:20220427T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/100
DESCRIPTION:Title: Smooth subalgebras in noncommutative geometry\nby Slawomir Kl
imek (Indiana University–Purdue University Indianapolis) as part of Nonc
ommutative geometry in NYC\n\n\nAbstract\nIn noncommutative geometry it is
often natural to consider dense *-subalgebras of C*-algebras in particula
r in connection with cyclic cohomology or with the study of unbounded deri
vations on C*-algebras.\nIf C*-algebras are thought of as generalizations
of topological spaces\, then dense subalgebras may be regarded as specifyi
ng additional structures on the underlying space\, like a smooth structure
.\nAt present there is no universally accepted general theory of such smoo
th subalgebras\, however there is a number of "standard" examples defined
and studied in the literature.\nIn analogy with the algebras of smooth fun
ctions on a compact manifold\, such a smooth subalgebra should have the fo
llowing properties:\n(1) It should be closed under holomorphic functional
calculus of all elements and under smooth-functional calculus of self-adjo
int elements\n(2) It should be complete with respect to a locally convex a
lgebra topology\nThe purpose of the talk is to discuss those concepts on e
xamples\, including some more recent constructions.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/100/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sherry Gong (Texas A&M University)
DTSTART:20220601T190000Z
DTEND:20220601T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/101
DESCRIPTION:Title: The Novikov conjecture\, operator K theory\, and diffeomorphism g
roups\nby Sherry Gong (Texas A&M University) as part of Noncommutative
geometry in NYC\n\n\nAbstract\nIn this talk\, I will discuss some recent
work on a version of the Novikov conjecture for certain subgroups of diffe
omorphism groups. This talk will be about joint work with Jianchao Wu\, Zh
izhang Xie\, and Guoliang Yu.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/101/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bhishan Jacelon (Czech Academy of Sciences)
DTSTART:20220608T190000Z
DTEND:20220608T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/102
DESCRIPTION:Title: Dynamical applications of C*-classification\nby Bhishan Jacel
on (Czech Academy of Sciences) as part of Noncommutative geometry in NYC\n
\n\nAbstract\nBy the work of many mathematicians\, including Elliott\, Gon
g\,\nLin and Niu\, the class of infinite-dimensional\, simple\, separable\
nC*-algebras that have finite nuclear dimension and satisfy the UCT can\nb
e classified by an invariant based on K-theory and traces. Insofar as\nthe
theme of classification is pervasive throughout science in\ngeneral\, and
(noncommutative) topology in particular\, this result is\nan extraordinar
y feat of mathematics. What's more\, it provides\npowerful machinery for t
he analysis of the internal structure of\namenable C*-algebras. In this ta
lk\, I will explain one such\napplication: In the subclass of classifiable
C*-algebras consisting of\nthose for which the simplex of tracial states
is nonempty\, with\nextremal boundary that is compact and has the structur
e of a connected\ntopological manifold\, automorphisms can be shown to be
generically\ntracially chaotic. Using similar ideas\, I will show how cert
ain stably\nprojectionless C*-algebras can be described as crossed product
s.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/102/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexey Kuzmin (University of Gothenburg)
DTSTART:20220615T190000Z
DTEND:20220615T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/103
DESCRIPTION:Title: Index theory of hypoelliptic operators on Carnot manifolds\nb
y Alexey Kuzmin (University of Gothenburg) as part of Noncommutative geome
try in NYC\n\n\nAbstract\nWe study the index theory of hypoelliptic operat
ors on Carnot manifolds -- manifolds whose Lie algebra of vector fields is
equipped with a filtration induced from sub-bundles of the tangent bundle
. A Heisenberg pseudodifferential operator\, elliptic in the calculus of v
an Erp-Yuncken\, is hypoelliptic and Fredholm. Under some geometric condit
ions\, we compute its Fredholm index by means of operator K-theory. These
results extend the work of Baum-van Erp (Acta Mathematica '2014) for co-or
iented contact manifolds to a methodology for solving this index problem g
eometrically on Carnot manifolds. Under the assumption that the Carnot man
ifold is regular\, i.e. has isomorphic osculating Lie algebras in all fibr
es\, and admits a flat coadjoint orbit\, the methodology derived from Baum
-van Erp's work is developed in full detail. In this case\, we develop K-t
heoretical dualities computing the Fredholm index by means of geometric K-
homology a la Baum-Douglas. The duality involves a Hilbert space bundle of
flat orbit representations. Explicit solutions to the index problem for T
oeplitz operators and operators of the form "ΔH+γT" are computed in geom
etric K-homology\, extending results of Boutet de Monvel and Baum-van Erp\
, respectively\, from co-oriented contact manifolds to regular polycontact
manifolds.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/103/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zhaoting Wei (Texas A&M-Commerce)
DTSTART:20220914T190000Z
DTEND:20220914T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/104
DESCRIPTION:Title: Equivariant K-theory on flag varieties of semisimple Lie groups\nby Zhaoting Wei (Texas A&M-Commerce) as part of Noncommutative geometr
y in NYC\n\n\nAbstract\nLet G be a real semisimple Lie group and X be the
flag variety of the complexification of G. Kashiwara proposed that there i
s a deep connection between G-equivariant sheaves on X and the representat
ions of G\, which plays the central role in geometric representation theor
y. In this talk I will discuss a K-theoretic analogue of G-equivariant she
aves\, namely G-equivariant K-theory on X. I will talk about attempts to c
ompute such K-theory and its relation with the representation theory of G.
I will do some computation in special cases.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/104/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kathryn McCormick (CSU Long Beach)
DTSTART:20220629T190000Z
DTEND:20220629T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/105
DESCRIPTION:Title: Holomorphic subalgebras of $n$-homogeneous $C^*$-algebras\nby
Kathryn McCormick (CSU Long Beach) as part of Noncommutative geometry in
NYC\n\n\nAbstract\nThere is a long tradition of analyzing $C^*$-algebras t
hrough topological invariants. One such result is Tomiyama and Takesaki's
1961 proof that an $n$-homogeneous $C^*$-algebra is determined up to $*$-i
somorphism by an underlying continuous matrix bundle. Suppose that the bas
e space of the bundle is a bordered Riemann surface with finitely many smo
oth boundary components\, and the interior of the bundle is holomorphic. T
hen for each such $n$-homogeneous $C^*$-algebra\, one can define a holomor
phic subalgebra. In this talk\, we will describe some progress made toward
s classifying these subalgebras up to complete isometric isomorphism based
on their underlying bundles\, including some recent work with Jacob Corne
jo.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/105/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniele Alessandrini (Columbia University)
DTSTART:20220921T190000Z
DTEND:20220921T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/106
DESCRIPTION:Title: Non commutative cluster coordinates for Higher Teichmüller Space
s\nby Daniele Alessandrini (Columbia University) as part of Noncommuta
tive geometry in NYC\n\n\nAbstract\nIn higher Teichmuller theory we study
subsets of the character varieties\nof surface groups that are higher rank
analogs of Teichmuller spaces\,\ne.g. the Hitchin components\, the spaces
of maximal representations and\nthe other spaces of positive representati
ons.\n\nFock-Goncharov generalized Thurston's shear coordinates and Penner
's\nLambda-lengths to the Hitchin components\, showing that they have a\nb
eautiful structure of cluster variety.\n\nWe applied a similar strategy to
Maximal Representations and we found new\ncoordinates on these spaces tha
t give them a structure of non-commutative\ncluster varieties\, in the sen
se defined by Berenstein-Rethak. This is based on a joint\nwork with Guich
ard\, Rogozinnikov and Wienhard and one with Berenstein\, Rethak\,\nRogozi
nnikov and Wienhard.\n\nIn an project in progress we are generalizing thes
e coordinates to the other\nsets of positive representations\, using some
tools we developed.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/106/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gabor Etesi (Budapest University of Technology and Economics)
DTSTART:20221026T190000Z
DTEND:20221026T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/107
DESCRIPTION:Title: The universal von Neumann algebra of smooth four-manifolds revisi
ted\nby Gabor Etesi (Budapest University of Technology and Economics)
as part of Noncommutative geometry in NYC\n\n\nAbstract\nMaking use of its
smooth structure only\, out of a connected\noriented smooth $4$-manifold
a von Neumann algebra is constructed. As a\nspecial four dimensional pheno
menon this von Neumann algebra contains\nalgebraic (i.e.\, formal or comin
g from a metric) curvature tensors of the\nunderlying $4$-manifold and the
von Neumann algebra itself is a\nhyperfinite factor of ${\\rm II}_1$-type
hence is unique up to abstract\nisomorphisms of von Neumann algebras. Ove
r a fixed $4$-manifold this\nuniversal von Neumann algebra admits a partic
ular representation on a\nHilbert space such that its unitary equivalence
class is preserved by\norientation-preserving diffeomorphisms consequently
the Murray--von\nNeumann coupling constant of this representation is well
-defined and gives\nrise to a new and computable real-valued smooth $4$-ma
nifold invariant.\nIts link with Jones' subfactor theory is noticed as wel
l as computations\nin the simply connected closed case are carried out.\n\
nApplication to the cosmological constant problem is also discussed.\nName
ly\, the aforementioned mathematical construction allows to reformulate\nt
he classical vacuum Einstein equation with cosmological constant over a\n$
4$-manifold as an operator equation over its tracial universal von\nNeuman
n algebra such that the trace of a solution is naturally identified\nwith
the cosmological constant. This framework permits to use the observed\nmag
nitude of the cosmological constant to estimate by topological means\nthe
number of primordial black holes about the Planck era. This number\nturns
out to be negligable which is in agreement with known density\nestimates b
ased on the Press--Schechter mechanism.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/107/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shirly Geffen (WWU Münster)
DTSTART:20221102T190000Z
DTEND:20221102T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/108
DESCRIPTION:Title: Dynamical comparison of amenable actions by non-amenable groups.<
/a>\nby Shirly Geffen (WWU Münster) as part of Noncommutative geometry in
NYC\n\n\nAbstract\nWe pull back boundary-type actions to paradoxical deco
mpositions of the acting group itself. \nIn particular\, we obtain strong
paradoxical structure in non-elementary hyperbolic groups\, in many lattic
es in Lie groups\, and in non-elementary Baumslag-Solitar groups.\nThis al
lows us to show that whenever such groups admit a minimal amenable topolog
ically free action on a compact Hausdorff space\, the system has dynamical
comparison and the attached crossed product is a purely infinite classifi
able C*-algebra.\n\nThis is joint work with Eusebio Gardella\, Julian Kran
z\, and Petr Naryshkin.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/108/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Victor Nistor (Université de Lorraine)
DTSTART:20221005T190000Z
DTEND:20221005T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/110
DESCRIPTION:Title: Invariant differential operators acting on quotient spaces and th
eir index\nby Victor Nistor (Université de Lorraine) as part of Nonco
mmutative geometry in NYC\n\n\nAbstract\nLet $G$ be a compact Lie group ac
ting on a smooth manifold $M$ (without \nbound
ary)\, $E \\to M$ be an equivariant bundle\, and $P$ be a $G$-invariant
\npseudodifferential operator acting on the sectio
ns of $E$. Let $\\alpha$ \nbe an irreducible r
epresentation of $G$ and $\\pi_\\alpha(P)$ be the restriction
\nof $P$ to the isotypical component corresponding to $\\alpha$.
We study the \nresulting algebra of symbols and w
e give a simple\, necessary and sufficient \ncrite
rion for $\\pi_\\alpha(P)$ to be Fredholm. We also provide a spectral
\nsequence converging to the periodic cyclic homolo
gy of the corresponding \nalgebra of symbols. T
his work was done in collaboration with A. Baldare\,
\nM. Benameur\, R. Come\, and M. Lesch.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/110/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Julian Kranz (WWU Münster)
DTSTART:20220928T190000Z
DTEND:20220928T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/111
DESCRIPTION:Title: K-theory of noncommutative Bernoulli shifts\nby Julian Kranz
(WWU Münster) as part of Noncommutative geometry in NYC\n\n\nAbstract\nGi
ven a unital C*-algebra A and a discrete group G\, we consider the shift a
ction of G on the infinite tensor product of G-many copies of A. In many c
ases\, we are able to compute the K-theory of the associated reduced cross
ed product (for instance when A is finite-dimensional and G is amenable).
The tools appearing include applications of the Baum-Connes conjecture and
elementary representation theory of finite groups. \nThis is joint work i
n progress with S. Chakraborty\, S. Echterhoff and S. Nishikawa.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/111/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Frei (University of Copenhagen)
DTSTART:20221012T190000Z
DTEND:20221012T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/112
DESCRIPTION:Title: Operator algebras and quantum information: Connes implies Tsirels
on and robust self-testing\nby Alexander Frei (University of Copenhag
en) as part of Noncommutative geometry in NYC\n\n\nAbstract\nWe give a ver
y simple proof of Connes implies Tsirelson\,\nand further advertise a hot
topic in quantum information: optimal states and robust self-testing. We s
howcase here how operator algebraic techniques can be quite fruitful.\n\nF
or this we begin with by recalling quantum strategies in the context of no
n-local games\, and their description in terms of the state space on the f
ull group algebra of certain free groups.\n\nWith this description at hand
\, we then directly obtain the main result via an elementary lifting resul
t by Kim\, Paulsen and Schafhauser:\nthe Connes embedding problem implies
the synchronous Tsirelson conjecture.\n\nAs such the entire proof is eleme
ntary\,\nand bypasses all versions of Kirchberg's QWEP conjecture and the
like\,\nas well as any reformulation such as in terms of the micro state c
onjecture.\n\nMoreover\, it should be (likely) easier to construct minimal
nonlocal games as counterexamples for the synchronous Tsirelson conjectur
e (which is equivalent to the full Tsirelson conjecture but in a non-trivi
al way) and so also nonamenable traces for above groups\, in other words n
on-Connes embeddable operator algebras.\n\n\n\nAfter this we continue (as
much as time permits) with an advertisement for one of the hottest topics
in quantum information:\ndevice-independent certification of quantum state
s\, or in short ROBUST SELF-TESTING\,\nwhich has tremendous importance for
the coming era of practical quantum computing.\nand we showcase how opera
tor algebraic techniques can be quite fruitful here.\n\nMore precisely\, w
e illustrate these techniques on the following two prominent classes of no
nlocal games:\n\n1) The tilted CHSH game.\nWe showcase here how to compute
the quantum value using operator algebraic techniques\, and how to use th
e same to derive uniqueness for entire optimal states\, including all high
er moments as opposed to correlations defined on two-moments only\, where
the latter compares to traditional self-testing.\nMoreover\, we report in
this example on previously unknown phase transitions on the uniqueness of
optimal states when varying the parameters for the tilted CHSH game.\n\n2)
The Mermin--Peres magic square and magic pentagram game.\nAs before\, we
also note here uniqueness of optimal states\, which in these two examples
is a basically familiar result.\n\nThe first part is based on preprint: ht
tps://arxiv.org/abs/2209.07940\nThe second part on self-testing (and furth
er robust self-testing) is based on joint work with Azin Shahiri.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/112/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mario Klisse (TU Delft)
DTSTART:20221019T190000Z
DTEND:20221019T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/113
DESCRIPTION:Title: On the isomorphism class of q-Gaussian C*-algebras\nby Mario
Klisse (TU Delft) as part of Noncommutative geometry in NYC\n\n\nAbstract\
nIn 1991 Bozejko and Speicher introduced a non-commutative version of Brow
nian motion by defining a family of algebras depending on a parameter −1
≤ q ≤ 1 that are nowadays commonly known as the q-Gaussian algebras.
These algebras interpolate between the extreme Bosonic case q = 1 and the
Fermionic case q = −1. For q = 0 they coincide with Voiculescu’s free
Gaussians. The q-Gaussians can be studied on the level of *-algebras\, on
the level of C*-algebras\, and on the level of von Neumann algebras. Where
as it is easily seen that in the *-algebraic setting the q-Gaussians all c
oincide\, as soon as one passes to the operator algebraic level the questi
on for the dependence on the parameter q becomes notoriously difficult.\n\
nAfter introducing the necessary background on q-Gaussians\, by considerin
g the so-called Akemann-Ostrand property of the canonical inclusion we wil
l discuss the dependence of the isomorphism class of q-Gaussian C*-algebra
s on the parameter q. This partially answers a question by Nelson and Zeng
.\n\nThe talk is baised on joint work with Matthijs Borst\, Martijn Casper
s and Mateusz Wasilewski.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/113/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergii Bezuglyi (University of Iowa)
DTSTART:20221115T190000Z
DTEND:20221115T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/114
DESCRIPTION:Title: Dynamics and measures on generalized Bratteli diagrams\nby Se
rgii Bezuglyi (University of Iowa) as part of Noncommutative geometry in
NYC\n\n\nAbstract\nIn the talk\, I discuss measures on the path space of\n
generalized Bratteli diagrams. We consider self-similar measures (called\n
also IFS measures) on the path space of discrete and measurable Bratteli\n
diagrams. In the literature\, similarity may be defined by systems of\naff
ine maps (Sierpinski) or systems of conformal maps (Julia). We study\nnew
classes of iterated function systems associated to stationary generalized\
nBratteli diagrams. For the corresponding iterated function\nsystems\, we
further identify the measures which are also shift-invariant.\nThe talk is
based on joint papers with Palle Jorgensen.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/114/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marcin Marciniak (University of Gdansk)
DTSTART:20221109T200000Z
DTEND:20221109T210000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/115
DESCRIPTION:Title: Positive maps on operator algebras – some problems and some sol
utions\nby Marcin Marciniak (University of Gdansk) as part of Noncommu
tative geometry in NYC\n\n\nAbstract\nIn the last decade\, the theory of p
ositive maps on operator algebras has gained increased importance as it ha
s been shown to have numerous applications in quantum information theory.
We will present an overview of the basic topics of this theory\, in partic
ular the characterization of extreme positive maps or the problem of decom
posability. One of the intensively studied recently problems is the questi
on of the existence of entangled PPT states with high Schmidt number. In t
he language of positive maps\, this is equivalent to the existence of inde
composable k-positive maps for large values of k.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/115/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Klaus Thomsen (Aarhus University)
DTSTART:20221130T200000Z
DTEND:20221130T210000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/116
DESCRIPTION:Title: The structure of KMS states for flows on an AF algebra\nby Kl
aus Thomsen (Aarhus University) as part of Noncommutative geometry in NYC\
n\n\nAbstract\nIn a recent work with George Elliott we have obtained a com
plete description of the configurations of KMS states that occur for flows
on a unital simple infinite dimensional AF algebra. The answer is that th
ey all do\, provided only that the simplex of 0-KMS states is affinely hom
eomorphic to the tracial state space of the AF algebra\; a condition which
is obviously necessary. In the talk I will explain the road to this concl
usion\, which can be seen as the culmination of work and ideas that go bac
k more than 40 years and has involved very many mathematicians.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/116/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andre Kornell (Dalhousie University)
DTSTART:20230125T200000Z
DTEND:20230125T210000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/117
DESCRIPTION:Title: Categories of Hilbert spaces\nby Andre Kornell (Dalhousie Uni
versity) as part of Noncommutative geometry in NYC\n\n\nAbstract\nHilbert
spaces form one category with bounded operators and another category with
contractions. I will present axioms for each of these two categories. Thes
e axioms are interesting because they make no explicit reference to the re
al number system. The proof appeals to Soler's theorem and to the theory o
f dagger categories\, as well as to a few familiar results from operator t
heory.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/117/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nikolai L. Vasilevski (CINVESTAV\, Mexico City)
DTSTART:20230201T200000Z
DTEND:20230201T210000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/118
DESCRIPTION:Title: Commutative algebras of Toeplitz operators on the disk: Spectral
theorem approach\nby Nikolai L. Vasilevski (CINVESTAV\, Mexico City) a
s part of Noncommutative geometry in NYC\n\n\nAbstract\nFor three standard
models of commutative algebras generated by Toeplitz\noperators in the we
ighted analytic Bergman space on he unit disk\, we\nfind their representat
ions as the algebras of bounded functions of\ncertain unbounded self-adjoi
nt operators. We discuss main properties of\nthese representation and\, es
pecially\, describe relations between\nproperties of the spectral function
of Toeplitz operators in the\nspectral representation and properties of t
he symbols.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/118/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Francesco D'Andrea (Università di Napoli Federico II)
DTSTART:20230208T200000Z
DTEND:20230208T210000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/120
DESCRIPTION:Title: CW structures in noncommutative geometry\nby Francesco D'Andr
ea (Università di Napoli Federico II) as part of Noncommutative geometry
in NYC\n\n\nAbstract\nI will illustrate some examples and ideas for a theo
ry of CW complexes in noncommutative geometry. In order to accommodate som
e important examples\, instead of diagrams in the category of quantum spac
es (dual to C*-algebras) one is forced to work with a suitable homotopy ca
tegory. In this category\, K-theory computations are made possible through
the use of a Mayer-Vietoris sequence. The K-theory of a quantum space can
be promoted from a plain abelian group to an augmented ring (in the sense
of Cartan-Eilenberg)\, giving a finer topological invariant. The construc
tion of this invariant suggests a notion of "topology" and "continuity" in
the quantum setting (a kind of Grothendieck topology). This is a work in
progress in collaboration with P.M. Hajac\, T. Maszczyk\, A. Sheu\, and B.
Zielinski.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/120/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christopher Wulff (University of Göttingen)
DTSTART:20230215T200000Z
DTEND:20230215T210000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/121
DESCRIPTION:Title: Generalized asymptotic algebras and E-theory for non-separable C*
-algebras\nby Christopher Wulff (University of Göttingen) as part of
Noncommutative geometry in NYC\n\n\nAbstract\nMany common ad hoc definitio
ns of bivariant K-theory for\nnon-separable C*-algebras have some kind of
drawback\, usually that one\ncannot expect the long exact sequences to hol
d in full generality. I\nwill present a way to define E-theory for non-sep
arable C*-algebras\nwithout such disadvantages via a generalized notion of
asymptotic\nalgebras. There is indication that canonical cycles of this n
ew model\nmight arise naturally in index theory on infinite dimensional ma
nifolds.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/121/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shanna Dobson (CSU Los Angeles)
DTSTART:20230105T140000Z
DTEND:20230105T150000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/122
DESCRIPTION:Title: Six Operations on Diamond Topos\nby Shanna Dobson (CSU Los An
geles) as part of Noncommutative geometry in NYC\n\n\nAbstract\nThis talk
is part of the Special Session on the Langlands Program\, JMM 2023 in Bost
on\, MA.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/122/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marina Prokhorova (Technion)
DTSTART:20230222T200000Z
DTEND:20230222T210000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/123
DESCRIPTION:Title: Index theory of unbounded Fredholm operators\nby Marina Prokh
orova (Technion) as part of Noncommutative geometry in NYC\n\n\nAbstract\n
Index theory for norm continuous families of bounded Fredholm operators wa
s developed in the classical work of Atiyah\; its analog for self-adjoint
operators was developed in the work of Atiyah and Singer. The index theory
of elliptic differential operators on closed manifolds is based on these
classical results: one can pass from operators of positive order to operat
ors of zeroth order\, and such a transformation is continuous.\n\nHowever\
, in other situations one needs to deal with weaker topologies on the spac
e of unbounded operators. For example\, for elliptic boundary value proble
ms on compact manifolds with boundary\, the graphs of corresponding unboun
ded operators depend continuously on parameter. The topology determined by
passing from a closed operator to its graph is called the graph topology.
The homotopy type of relevant spaces of unbounded Fredholm operators was
determined by M. Joachim in 2003.\n\nMy talk is devoted to an index theory
of graph continuous families of unbounded Fredholm operators in a Hilbert
space. I will show how this theory is related to the classical index theo
ry of bounded Fredholm operators. The talk is based on my recent preprints
arXiv:2110.14359 and arXiv:2202.03337.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/123/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Feodor Kogan (University of Toronto)
DTSTART:20230301T200000Z
DTEND:20230301T210000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/124
DESCRIPTION:Title: Overview of Cartan subalgebras in operator algebras\nby Feodo
r Kogan (University of Toronto) as part of Noncommutative geometry in NYC\
n\n\nAbstract\nSimilar to the setting of Lie algebras\, a Cartan subalgebr
a in a C*-algebra is a maximal abelian subalgebra with some additional pro
perties. Unlike the setting of Lie algebras Cartan subalgebras might not e
xist\, and if they do\, they are rarely unique. I will give an overview of
old and new results concerning Cartan subalgebras in C*-algebras with an
emphasis on their relation to groupoids.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/124/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christian Voigt (University of Glasgow)
DTSTART:20230308T200000Z
DTEND:20230308T210000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/125
DESCRIPTION:Title: Infinite quantum permutations\nby Christian Voigt (University
of Glasgow) as part of Noncommutative geometry in NYC\n\n\nAbstract\nQuan
tum symmetries feature naturally in the study of quantum groups\, subfacto
rs and quantum information. In this talk I will present an approach to stu
dy quantum symmetries of infinite graphs. This leads to new examples of di
screte quantum groups\, linking naturally with previous work in the case o
f finite graphs. I will discuss a number of concrete examples\, and also h
ighlight some intriguing open problems.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/125/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Severino T. Melo (Universidade de São Paulo)
DTSTART:20230315T190000Z
DTEND:20230315T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/126
DESCRIPTION:Title: Pseudodifferential operators in strict deformation quantization\nby Severino T. Melo (Universidade de São Paulo) as part of Noncommuta
tive geometry in NYC\n\n\nAbstract\nMost of the talk will be about old res
ults of H. O. Cordes\, Marcela Merklen and myself about characterizations
of pseudodifferential\noperators as smooth vectors for actions of the Heis
enberg group. Then I will announce related results recently obtained with
Rodrigo Cabral and Michael Forger\nabout a class of pseudodifferential ope
rators with $C^*$-algebra-valued symbols introduced by M. Rieffel in his c
onstruction of a "strict deformation\nquantization" for a $C^*$-algebra wi
th an action of $R^n$. We have proven the uniqueness of the $C^*$-norm for
Rieffel's (non complete) algebra and have\nalso proven a conjecture of Ri
effel which characterizes his pseudodifferential operators as the smooth v
ectors for an action of the Heisenberg group.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/126/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexei Yu. Pirkovskii (HSE Moscow)
DTSTART:20230329T190000Z
DTEND:20230329T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/127
DESCRIPTION:Title: Nonformal deformations of algebras of holomorphic functions\n
by Alexei Yu. Pirkovskii (HSE Moscow) as part of Noncommutative geometry i
n NYC\n\n\nAbstract\nFormal deformations of associative algebras are by no
w classical and relatively well-studied objects. They were introduced by G
erstenhaber in 1964\, and they are interesting especially because of their
relation to deformation quantization. By contrast\, the theory of nonform
al deformations is now at a much earlier stage of development. Roughly\,
a general feature of all existing approaches to nonformal deformations\, w
hich distinguishes them from formal deformations\, is that the role of the
"base" ring is now played by a certain algebra of functions (continuous\,
or smooth\, or holomorphic...) rather than by the algebra of formal power
series. This makes nonformal deformations quite attractive from the physi
cal point of view\, because they allow evaluating the deformed star produc
t at concrete nonzero values of the deformation parameter (Planck's consta
nt). In this talk\, our main objects will be nonformal (or\, more exactly\
, holomorphic) deformations of the algebras of holomorphic functions on th
e polydisc and on the ball in $\\mathbb{C}^n$. We will discuss some proper
ties of such deformations and their relation to formal deformations. If ti
me permits\, we will compare our approach to holomorphic deformations with
S. Waldmann's approach\, which is better adapted to deformation quantizat
ion\, but which applies only to some proper subalgebras of the algebras of
holomorphic functions.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/127/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Elias G. Katsoulis (East Carolina University)
DTSTART:20230419T190000Z
DTEND:20230419T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/128
DESCRIPTION:Title: Isomorphisms and stable isomorphisms of non-selfadjoint operator
algebras\nby Elias G. Katsoulis (East Carolina University) as part of
Noncommutative geometry in NYC\n\n\nAbstract\nIn this talk we address isom
orphisms and stable isomorphisms of various\nclasses of operator algebras.
We state and resolve the isomorphism problem for\ntensor algebras of unit
al multivariable dynamical systems. Specifically we show\nthat unitary equ
ivalence after a conjugation for multi-variable dynamical systems\nis a co
mplete invariant for complete isometric isomorphisms between their tensor\
nalgebras. In particular\, this settles a conjecture of Davidson and Kakar
iadis relating\nto work of Arveson from the sixties\, and extends related
work of Kakariadis and\nKatsoulis.\n\nWe also address stable isomorphism o
f operator algebras\, in connection with a\nrecent work of Dor-On\, Eilers
and Geffen. Among others we show that if $\\mathcal{A}$\n and $\\mathcal{
B}$ are operator algebras with diagonals isomorphic to $c_0$ and \n$\\math
cal{K}$ are the compact\noperators\, then $\\mathcal{A}\\otimes\\mathcal{K
}$ and $\\mathcal{B}\\otimes\\mathcal{K}$\nare isometrically isomorphic if
and only if $\\mathcal{A}$ and\n$\\mathcal{B}$ are isometrically isomorph
ic. If the algebras $\\mathcal{A}$ and $\\mathcal{B}$ satisfy an extra ana
lyticity\ncondition\, a similar result holds with $\\mathcal{K}$ being rep
laced by any operator algebra\ncontaining the compact operators. Time perm
itting we will discuss other classes\nof operator algebras and their stabl
e isomorphisms\, including tensor algebras of\nmultivariable dynamical sys
tems.\n\nThe above results come from various projects with C. Ramsey\, E.
Kakariadis\nand X. Lin.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/128/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anar Dosi (Middle East Technical University\, Cyprus)
DTSTART:20230412T170000Z
DTEND:20230412T180000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/129
DESCRIPTION:Title: Projective positivity of the function systems\nby Anar Dosi (
Middle East Technical University\, Cyprus) as part of Noncommutative geome
try in NYC\n\n\nAbstract\nThe present talk is devoted to the projective po
sitivity in the category of function systems. It is an operator positivity
occurred in the quantization problems of the operator systems. It turns o
ut that every $∗$-(poly)normed topology compatible with a duality result
s in the (local) projective positivity given by a filter base of the unita
l cones with its separated intersection. We describe the (local) projectiv
e positivity of the (local) $L^{p}$-spaces given by a bounded (or unbounde
d) positive Radon measure on a locally compact topological space. The geom
etry of the related state spaces is described in the case of $L^{p}$-space
s\, Schatten matrix spaces\, and $L^{p}$-spaces of a finite von Neumann al
gebra.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/129/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dimitris Gerontogiannis (Leiden University)
DTSTART:20230426T190000Z
DTEND:20230426T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/130
DESCRIPTION:Title: Smale spaces and their dimension theory\nby Dimitris Gerontog
iannis (Leiden University) as part of Noncommutative geometry in NYC\n\n\n
Abstract\nSmale spaces were defined by David Ruelle in the 1970's as topol
ogical models for the typically fractal-like hyperbolic nonwandering sets
of Stephen Smale's Axiom A systems. A Smale space is a compact metric spac
e together with a homeomorphism having exponential contraction and expansi
on behaviour. Prototype examples are the topological Markov chains\, aperi
odic substitution tilings and hyperbolic toral automorphisms. This talk wi
ll give an example-driven introduction to Smale spaces with a focus on the
ir dimension theory\, which can be studied via Markov partitions and Ahlfo
rs regular measures. If time permits\, I will briefly mention how the dime
nsion theory of a Smale space is related to fine analytic properties of th
e operator algebras encoding the stable and unstable foliations on it.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/130/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ali Raad (KU Leuven)
DTSTART:20230517T190000Z
DTEND:20230517T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/131
DESCRIPTION:Title: Inductive Limit Cartan Subalgebras\nby Ali Raad (KU Leuven) a
s part of Noncommutative geometry in NYC\n\n\nAbstract\nIn recent years th
e interest for Cartan subalgebras in C*-algebras has risen due to new conn
ections found with topological dynamics and geometric group theory\, as we
ll as the classification programme for C*-algebras. For this\, the study o
f Cartan subalgebras in inductive limit C*-algebras is fundamental. I will
give an overview of this topic as well as provide some new existence and
uniqueness results for inductive limit Cartan subalgebras.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/131/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ulrich Bunke (Universität Regensburg)
DTSTART:20230524T190000Z
DTEND:20230524T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/132
DESCRIPTION:Title: A homotopical view on $K$ and $KK$-theory for $C^{*}$-algebras\nby Ulrich Bunke (Universität Regensburg) as part of Noncommutative geo
metry in NYC\n\n\nAbstract\nThe goal of this talk is to motivate the consi
deration of spectrum-valued K-theory for $C^{*}$-algebras. To this end I w
ill discuss some examples where the spectrum-valued functor helps to simp
lify classical statements and their justification. I will then explain ho
w to construct a spectrum-valued $K$-theory functor using a homotopical r
efinement of KK-theory. Accepting the language of $\\infty$-categories\, t
he latter can be obtained in a straightforward way by forcing the desire
d universal properties.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/132/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arthur Pander Maat (Queen Mary University)
DTSTART:20230913T190000Z
DTEND:20230913T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/133
DESCRIPTION:Title: Hilbert Modules over C*-categories\nby Arthur Pander Maat (Qu
een Mary University) as part of Noncommutative geometry in NYC\n\n\nAbstra
ct\nC*-categories are a ‘horizontal categorification’ of C*-algebras\,
and they have a theory of Hilbert modules which generalizes that over C*-
algebras. We go through some results about these modules\, culminating in
an Eilenberg-Watts theorem that characterizes which functors between modul
e categories are given by tensor products. We finish with some new work em
ploying this result\, along with work of Benjamin Duenzinger’s\, to exhi
bit a localization of the category of locally small C*-categories at the M
orita equivalences.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/133/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bernard Russo (UC Irvine)
DTSTART:20230906T190000Z
DTEND:20230906T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/134
DESCRIPTION:Title: Anti-$C^*$-algebras\nby Bernard Russo (UC Irvine) as part of
Noncommutative geometry in NYC\n\n\nAbstract\nWe introduce a class of Bana
ch algebras that we call\nanti-$C^*$-algebras. We show that the normed st
andard embedding of a\n$C^*$-ternary ring is the direct sum of a $C^*$-alg
ebra and an\nanti-$C^*$-algebra. We prove that C*-ternary rings and anti-$
C^*$-algebras are\nsemisimple. We give two new characterizations of $C^*$-
ternary rings which\nare isomorphic to a TRO (ternary ring of operators)\,
providing answers\nto a query raised by Zettl in 1983\, and we propose so
me problems for\nfurther study. (Joint work with Robert Pluta)\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/134/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gihyun Lee (Ghent University)
DTSTART:20230920T190000Z
DTEND:20230920T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/135
DESCRIPTION:Title: $L_p$-bounds for pseudodifferential operators on curved noncommut
ative tori\nby Gihyun Lee (Ghent University) as part of Noncommutative
geometry in NYC\n\n\nAbstract\nIn the theory of pseudodifferential operat
ors\, one of the most essential topics is the study of mapping properties
of pseudodifferential operators between various kinds of function spaces.
The investigation of $L_p$-boundedness of pseudodifferential operators is
particularly important\, considering its consequences for the regularity a
nd existence of solutions of PDEs.\n\nThe purpose of this talk is to discu
ss the counterpart of this problem on noncommutative tori. Noncommutative
tori are the most intensively studied noncommutative spaces in noncommutat
ive geometry and arise in various parts of mathematics and mathematical ph
ysics. Pseudodifferential calculus on noncommutative tori was introduced i
n early 1980s by A. Connes\, and it has emerged as an indispensable tool i
n the recent study of differential geometry of noncommutative tori. Meanwh
ile\, J. Rosenberg introduced the notion of Riemannian metric on noncommut
ative tori a decade ago. In this talk\, I will first recall the notion of
a curved noncommutative torus\, i.e.\, a noncommutative torus endowed with
a Riemannian metric in the sense of J. Rosenberg. I will then show the bo
undedness of pseudodifferential operators on noncommutative $L_p$-spaces a
ssociated with the volume form induced by a Riemannian metric. Based on jo
int work with V. Kumar.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/135/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pawel Sarkowicz (University of Ottawa)
DTSTART:20230927T190000Z
DTEND:20230927T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/136
DESCRIPTION:Title: Tensorially absorbing inclusions of C*-algebras\nby Pawel Sar
kowicz (University of Ottawa) as part of Noncommutative geometry in NYC\n\
n\nAbstract\nWe introduce the notion of a tensorially absorbing inclusion
-- that is\, when an inclusion absorbs a strongly self-absorbing C*-algebr
a in a suitable way. We discuss various properties\, central sequence char
acterizations\, give examples and non-examples\, and provide some applicat
ions and natural open questions.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/136/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Charlie Beil (University of Graz)
DTSTART:20231004T190000Z
DTEND:20231004T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/137
DESCRIPTION:Title: Nonnoetherian geometry\, noncommutative desingularizations\, and
quantum theory\nby Charlie Beil (University of Graz) as part of Noncom
mutative geometry in NYC\n\n\nAbstract\nI will introduce a new kind of geo
metry that arises from nonnoetherian subalgebras of polynomial rings\, and
\, more generally\, coordinate rings of affine varieties. In this construc
tion\, points may be 'smeared-out' and have positive dimension. I will the
n describe an application of this geometry to a class of noncommutative al
gebras defined by oriented graphs in surfaces\, called dimer and ghor alge
bras. The geometry allows these algebras to be viewed as noncommutative de
singularizations of their centers\, and yields relationships between their
representation theory and the surface topology. Finally\, I will sketch a
n application of the geometry to a new spacetime model of spin and its wav
e function collapse.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/137/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joakim Arnlind (Linköping University)
DTSTART:20231011T190000Z
DTEND:20231011T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/138
DESCRIPTION:Title: Noncommutative Riemannian Geometry of Kronecker Algebras\nby
Joakim Arnlind (Linköping University) as part of Noncommutative geometry
in NYC\n\n\nAbstract\nDifferential calculus in noncommutative geometry com
e in several different flavors\, and one of the more concrete versions goe
s by the name of derivation based differential calculus. This calculus is
built from a disinguished Lie algebra of derivations\, and lead to the for
mulation of differential forms\, cohomology and connections. A fundamental
question in noncommutative Riemannian geometry is the existence and uniqu
eness of a torsion free and metric compatible connection\; i.e a Levi-Civi
ta connection. For the moment\, there are no general results addressing th
is question in this context\, and I will present a case study based on a s
imple quiver path algebra\, and show how the existence of a Levi-Civita co
nnection depend on the choice of a Lie algebra of derivations.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/138/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wade Bloomquist (Morningside University)
DTSTART:20231018T190000Z
DTEND:20231018T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/139
DESCRIPTION:Title: Quantum Traces and Degenerations\nby Wade Bloomquist (Morning
side University) as part of Noncommutative geometry in NYC\n\n\nAbstract\n
Skein algebras of surfaces describe a multiplication for curves on surface
s\, which remembers the poisson structure on the ring of regular functions
of the character variety of the surface. Quantum trace maps\, introduced
by Bonahon and Wong\, show how skein algebras of punctured surfaces can b
e embedded into well-behaved algebras called quantum tori. Our discussion
will focus on a joint generalization of skein algebras\, which captures t
he hyperbolic geometry seen in Roger-Yang skein algebras and the quantum g
roup comodule structure seen in stated skein algebras. This generalizatio
n is a key tool in building a quantum trace map for degenerations (coming
from filtrations) of skein algebras of closed surfaces. As time permits w
e will discuss some applications. A strong effort will be made to introdu
ce these topics at the expense of some technical details. This work is jo
int with Thang Le and Hiroaki Karuo.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/139/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jesse Peterson (Vanderbilt University)
DTSTART:20231101T190000Z
DTEND:20231101T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/140
DESCRIPTION:Title: Biexact groups and von Neumann algebras\nby Jesse Peterson (V
anderbilt University) as part of Noncommutative geometry in NYC\n\n\nAbstr
act\nThe notion of biexactness for groups was introduced by Ozawa in 2004
and has since become one of the major tools for studying decomposability p
roperties for von Neumann algebras. I will survey the development of biexa
ctness over the last two decades\, and I will discuss a joint project with
Changying Ding where we introduce biexact von Neumann algebras and frame
many of these results in this more general setting.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/140/
END:VEVENT
BEGIN:VEVENT
SUMMARY:N. Christopher Phillips (University of Oregon and Fields Institute
for Research in Mathematical Sciences)
DTSTART:20231025T190000Z
DTEND:20231025T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/141
DESCRIPTION:Title: The radius of comparison of C (X) is about half the covering dime
nsion of X\nby N. Christopher Phillips (University of Oregon and Field
s Institute for Research in Mathematical Sciences) as part of Noncommutati
ve geometry in NYC\n\n\nAbstract\nRecall that a C*-algebra $A$ has strict
comparison of projections\nif whenever $p$ and $q$ are projections in matr
ix algebras over $A$\,\nand $\\tau (p) < \\tau (q)$ for all tracial states
$\\tau$ on $A$\,\nthen $p$ is Murray-von Neumann subequivalent to $q$.\nI
n connection with the Elliott\nclassification program\, and because many s
imple C*-algebras have\nvery few projections\, this has been extended to c
omparison of\ngeneral positive elements.\n(This will be explained in the t
alk.)\nStrict comparison holds\nfor unital stably finite classifiable simp
le C*-algebras.\nThe radius of comparison ${\\mathrm{rc}} (A)$ of a C*-alg
ebra $A$\nis a numerical measure of the failure of strict comparison.\nIt
is zero if strict comparison holds\,\nand in general is a not so well unde
rstood kind of topological dimension.\n\nLet $X$ be a compact metric space
.\nIt has been known for some time that ${\\mathrm{rc}} (C (X))$\nis at mo
st about half the covering dimension of $X$.\nIn 2013\, Elliott and Niu pr
oved that ${\\mathrm{rc}} (C (X))$ is\,\nup to an additive constant\,\nat
least half the rational cohomological dimension of $X$.\nRecently\, we pro
ved that\, up to a slightly worse additive constant\,\n${\\mathrm{rc}} (C
(X))$ is at least half the covering dimension of $X$\,\nwhich is sometimes
much larger.\nThis shows that ${\\mathrm{rc}} (A)$\, like stable rank\, r
oughly\ncorresponds to covering dimension\, not to rational or integral\nc
ohomological dimension\, and not to some previously unknown dimension.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/141/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Iason Moutzouris (Purdue University)
DTSTART:20231115T200000Z
DTEND:20231115T210000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/142
DESCRIPTION:Title: When amenable groups have real rank zero $C^*$-algebras?\nby
Iason Moutzouris (Purdue University) as part of Noncommutative geometry in
NYC\n\n\nAbstract\nFor every torsion free\, discrete and amenable group $
G$\, the Kadison-Kaplansky conjecture has been verified\, so $C^*(G)$ has
no nontrivial projections. On the other hand\, every torsion element $g\\i
n G$\, of order $n$\, gives rise to a projection $\\frac{1+g+...+g^{n-1}}{
n}\\in C^*(G)$. Actually\, if $G$ is locally finite\, then $C^*(G)$ is an
AF-algebra\, so it has an abundance of projections. So\, it is natural to
ask what happens when the group has both torsion and\nnon-torsion element
s. A result on this direction came from Scarparo\, who showed that for eve
ry discrete\, infinite\, finitely generated elementary amenable group\, $
C^*(G)$ cannot have real rank zero. In this talk\, we will explain why if
$G$ is discrete\, amenable and $C^*(G)$ has real rank zero\, then all elem
entary amenable normal subgroups with finite Hirsch length must be locally
finite.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/142/
END:VEVENT
BEGIN:VEVENT
SUMMARY:N. Christopher Phillips (University of Oregon)
DTSTART:20240507T190000Z
DTEND:20240507T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/143
DESCRIPTION:Title: Minicourse: An invitation to mean dimension of a dynamical syste
m and the radius of comparison of its crossed product\, I\nby N. Chr
istopher Phillips (University of Oregon) as part of Noncommutative geometr
y in NYC\n\n\nAbstract\nPrerequisites (optional): \n\n1. https://sju.webex
.com/recordingservice/sites/sju/recording/e0819482c399103cbf7c005056812d4c
/playback\n\n2. https://sju.webex.com/recordingservice/sites/sju/recording
/480a92c95598103cae68005056819173/playback\n\n\nThe purpose of this minico
urse is to explain the background\n(including the terms below) and some pr
ogress towards the following conjecture\, relating topological dynamics to
the structure of the crossed product $C^*$-algebra.\n\nLet $G$ be a count
able amenable group\, let $X$ be a compact metrizable space\,\nand let $T$
be an action of $G$ on $X$. The mean dimension $mdim ~(T)$ is a \npurely
dynamical invariant\, designed so that the mean dimension of the shift \no
n $([0\, 1]^d)^G$ is equal to $d$. The radius of comparison $rc ~(A)$ of a
\nunital $C^*$-algebra $A$ is a numerical measure of failure of compariso
n\nin the Cuntz semigroup of $A$\, a generalization of unstable K-theory.\
nIt was introduced to distinguish $C^*$-algebras having no connection\nwit
h dynamics. The conjecture asserts that if $T$ is free and minimal\,\nthen
$rc ~(C^* (G\, X\, T)) = \\frac{1}{2} ~mdim ~(T)$. The inequality\n$rc ~(
C^* (G\, X\, T)) \\leq \\frac{1}{2} ~mdim ~(T)$ is known for \n$G = {\\mat
hbb{Z}}^n$\, and progress towards the inequality\n$rc ~(C^* (G\, X\, T)) \
\geq \\frac{1}{2} ~mdim ~(T)$ has been made for the known \nclasses of exa
mples of free minimal actions with nonzero mean dimension\,\nfor any count
able amenable group $G$. The emphasis will be on the inequality\n$rc ~(C^*
(G\, X\, T)) \\geq \\frac{1}{2} ~mdim ~(T)$\;\nthe results there are join
t work with Ilan Hirshberg.\n\n\nLecture 1. \n\nThis lecture will be mainl
y about dynamical systems.\nAfter an introduction\, we will review the cro
ssed product $C^*$-algebra associated to a\ndynamical system\, and then de
scribe the mean dimension of a dynamical system.\nTime permitting\, we wil
l start the discussion of comparison of projections in \n$C^*$-algebras.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/143/
END:VEVENT
BEGIN:VEVENT
SUMMARY:N. Christopher Phillips (University of Oregon)
DTSTART:20240514T190000Z
DTEND:20240514T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/144
DESCRIPTION:Title: Minicourse: An invitation to mean dimension of a dynamical system
and the radius of comparison of its crossed product\, II\nby N. Chr
istopher Phillips (University of Oregon) as part of Noncommutative geometr
y in NYC\n\n\nAbstract\nThe purpose of this minicourse is to explain the b
ackground\n(including the terms below) and some progress towards the follo
wing conjecture\, relating topological dynamics to the structure of the cr
ossed product $C^*$-algebra.\n\nLet $G$ be a countable amenable group\, le
t $X$ be a compact metrizable space\,\nand let $T$ be an action of $G$ on
$X$. The mean dimension $mdim ~(T)$ is a \npurely dynamical invariant\, de
signed so that the mean dimension of the shift \non $([0\, 1]^d)^G$ is equ
al to $d$. The radius of comparison $rc ~(A)$ of a \nunital $C^*$-algebra
$A$ is a numerical measure of failure of comparison\nin the Cuntz semigrou
p of $A$\, a generalization of unstable K-theory.\nIt was introduced to di
stinguish $C^*$-algebras having no connection\nwith dynamics. The conjectu
re asserts that if $T$ is free and minimal\,\nthen $rc ~(C^* (G\, X\, T))
= \\frac{1}{2} ~mdim ~(T)$. The inequality\n$rc ~(C^* (G\, X\, T)) \\leq \
\frac{1}{2} ~mdim ~(T)$ is known for \n$G = {\\mathbb{Z}}^n$\, and progres
s towards the inequality\n$rc ~(C^* (G\, X\, T)) \\geq \\frac{1}{2} ~mdim
~(T)$ has been made for the known \nclasses of examples of free minimal ac
tions with nonzero mean dimension\,\nfor any countable amenable group $G$.
The emphasis will be on the inequality\n$rc ~(C^* (G\, X\, T)) \\geq \\fr
ac{1}{2} ~mdim ~(T)$\;\nthe results there are joint work with Ilan Hirshbe
rg.\n\nLecture 2.\n\nThis lecture will be mainly about comparison in $C^*$
-algebras.\nWe will describe comparison properties\, first for projections
and then for positive elements.\nThen we define the radius of comparison\
, and show how it is related to ``noncommutative dimension''.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/144/
END:VEVENT
BEGIN:VEVENT
SUMMARY:N. Christopher Phillips (University of Oregon)
DTSTART:20240521T190000Z
DTEND:20240521T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/145
DESCRIPTION:Title: Minicourse: An invitation to mean dimension of a dynamical syste
m and the radius of comparison of its crossed product\, III\nby N. C
hristopher Phillips (University of Oregon) as part of Noncommutative geome
try in NYC\n\n\nAbstract\nThe purpose of this minicourse is to explain the
background\n(including the terms below) and some progress towards the fol
lowing conjecture\, relating topological dynamics to the structure of the
crossed product $C^*$-algebra.\n\nLet $G$ be a countable amenable group\,
let $X$ be a compact metrizable space\,\nand let $T$ be an action of $G$ o
n $X$. The mean dimension $mdim ~(T)$ is a \npurely dynamical invariant\,
designed so that the mean dimension of the shift \non $([0\, 1]^d)^G$ is e
qual to $d$. The radius of comparison $rc ~(A)$ of a \nunital $C^*$-algebr
a $A$ is a numerical measure of failure of comparison\nin the Cuntz semigr
oup of $A$\, a generalization of unstable K-theory.\nIt was introduced to
distinguish $C^*$-algebras having no connection\nwith dynamics. The conjec
ture asserts that if $T$ is free and minimal\,\nthen $rc ~(C^* (G\, X\, T)
) = \\frac{1}{2} ~mdim ~(T)$. The inequality\n$rc ~(C^* (G\, X\, T)) \\leq
\\frac{1}{2} ~mdim ~(T)$ is known for \n$G = {\\mathbb{Z}}^n$\, and progr
ess towards the inequality\n$rc ~(C^* (G\, X\, T)) \\geq \\frac{1}{2} ~mdi
m ~(T)$ has been made for the known \nclasses of examples of free minimal
actions with nonzero mean dimension\,\nfor any countable amenable group $G
$. The emphasis will be on the inequality\n$rc ~(C^* (G\, X\, T)) \\geq \\
frac{1}{2} ~mdim ~(T)$\;\nthe results there are joint work with Ilan Hirsh
berg.\n\n\nLecture 3.\n\nIn this lecture\, we state some known results tow
ards the conjecture \n$rc ~(C^* (G\, X\, T)) = \\frac{1}{2} ~mdim ~(T)$\,\
nand say something about the ideas which go into the results\ntowards the
inequality $rc ~(C^* (G\, X\, T)) \\geq \\frac{1}{2} ~mdim ~(T)$.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/145/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Skeide (Università degli Studi del Molise)
DTSTART:20231129T200000Z
DTEND:20231129T210000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/146
DESCRIPTION:Title: Partial Isometries Between Hilbert Modules\nby Michael Skeide
(Università degli Studi del Molise) as part of Noncommutative geometry i
n NYC\n\n\nAbstract\nHilbert modules are Banach spaces and share\, of cour
se\, all their good properties. But geometrically they behave - as opposed
with the very well-behaved Hilbert spaces - very much like pre-Hilbert sp
aces.\n\nAs a common root of most problems - if not all - one may highlig
ht the fact that Hilbert modules need not be self-dual\; one of the most s
triking consequences of missing self-duality is the fact that not all boun
ded modules maps need to possess an adjoint. (Intimately related: not all
closed submodules are the range of a projection.) This raises the question
how to define isometries\, cosisometries\, and partial isometries between
Hilbert modules\, without requiring explicitly in the definition that the
se maps are adjointable.\n\nWhile the definition of isometries (as inner p
roduct preserving maps) is rather natural and well-known since long (they
need not be adjointable)\, our definitions (proposed with Orr Shalit) of c
oisometries (they turn out to be adjointable) and partial isometries (they
need not be adjointable) are rather recent.\n\nAs a specific problem\, we
will address the question how to find a (reasonable) composition law amon
g partial isometries (making them the morphisms of a category). It turns o
ut that for Hilbert spaces the problem can be solved\, while for Hilbert m
odules we have to pass to the *partially defined* isometries. The proofs o
f some of the intermediate statements explore typical features of proofs i
n Hilbert module theory: Some are like those for Hilbert spaces\; some red
uce the proof (by means of a well-known technical tool) to that for Hilber
t spaces\; and some are simply ``different''. (Of course\, the latter also
for work Hilbert spaces\; but they are ``different'' from what you would
write down with all you arsenal of Hilbert space methods at your disposal.
)\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/146/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vladimir Manuilov (Moscow State University)
DTSTART:20231122T200000Z
DTEND:20231122T210000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/147
DESCRIPTION:Title: Metrics on doubles as an inverse semigroup\nby Vladimir Manui
lov (Moscow State University) as part of Noncommutative geometry in NYC\n\
n\nAbstract\nUsually metrics do not form an algebraic structure. I was int
erested in various metrics on two copies (double) of a metric space $(X\,d
)$ such that the metric on each copy is $d$\, and only distances between p
oints on different copies of $X$ may vary. To my surprise\, if one passes
from metrics to their equivalence classes (either quasi-equivalence or coa
rse equivalence) then the metrics on the double of $X$ form an inverse sem
igroup. Inverse semigroups are similar to sets of partial isometries on a
Hilbert space\, and one may define a C*-algebra of an inverse semigroup al
ong the same guidelines as group C*-algebras. I shall speak about some res
ults on these inverse semigroups\, e.g. when they are commutative\, and wh
en they have a kind of finiteness property\, i.e. when the unit is Murray-
von Neumann equivalent to a proper projection.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/147/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Benjamin Steinberg (City College of New York)
DTSTART:20231206T200000Z
DTEND:20231206T210000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/148
DESCRIPTION:Title: Simplicity of inverse semigroup and etale groupoid algebras\n
by Benjamin Steinberg (City College of New York) as part of Noncommutative
geometry in NYC\n\n\nAbstract\nWe survey some of the results on simplicit
y of algebras of ample groupoids over fields\, culminating with the defini
tive results of the speaker and Szakacs. We indicate some applications to
an old question of Munn from the 70s on simplicity of inverse semigroups
algebras and to Nekrashevych algebras of self-similar groups.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/148/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Francis (University of Western Ontario)
DTSTART:20240124T200000Z
DTEND:20240124T210000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/149
DESCRIPTION:Title: Holonomy and the Newlander-Nirenberg theorem in $b^k$-geometry\nby Michael Francis (University of Western Ontario) as part of Noncommut
ative geometry in NYC\n\n\nAbstract\nMelrose introduced $b$-geometry as a
paradigm for studying operators on a manifold that suffer a first-order de
generacy along a hypersurface. Scott considered higher-order degeneracies\
, introducing $b^k$-geometry for $k>1$. In this talk we consider two diffe
rent aspects of (a slight variation of) Scott's $b^k$-geometry: one global
and one local. Firstly\, we discuss the classification of $b^k$-geometrie
s by a holonomy invariant (similar results were obtained independently by
Bischoff-del Pino-Witte). We also discuss the Newlander-Nirenberg for comp
lex $b^k$-manifolds. Complex $b$-manifolds ($k=1$) were defined by Mendoza
the Newlander-Nirenberg theorem for $b$-manifolds was obtained by Francis
-Barron.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/149/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Damián Ferraro (Departamento de Matemática y Estadística del Li
toral\, Uruguay)
DTSTART:20240207T200000Z
DTEND:20240207T210000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/150
DESCRIPTION:Title: Cross-sectional C*-algebras of Fell bundles\nby Damián Ferra
ro (Departamento de Matemática y Estadística del Litoral\, Uruguay) as p
art of Noncommutative geometry in NYC\n\n\nAbstract\nA Fell bundle (or C*-
algebraic bundle) $B=\\{B_t\\}_{t\\in G}$ may be thought of as a kind of a
ction of the base group $G$ on the C*-algebra $B_e$\, $e$ being the unit o
f $G.$ When doing so\, the full and reduced cross-sectional C*-algebras of
$B$\, $C^*(B)$ and $C^*_r(B)$ respectively\, become the full and reduced
crossed products of the action.\n\nIt is implicit in Exel-Ng's constructio
n/characterization of $C^*_r(B)$ that the induction of representations fro
m $H:=\\{e\\}$ to $G\,$ $U\\mapsto Ind_{H\\uparrow G}(U)\,$ and from $B_e$
to $B\,$ $T\\mapsto Ind_{B_e\\uparrow B}(T)\,$ are intimately related and
that both can be used to define/describe $C^*_r(B).$ If $B$ is saturated\
, the equivalence of the definitions is a straightforward consequence of F
ell's absorption principle.\n\nThe situation is not so clear when one cons
iders closed subgroups $H$ of $G$ other than $\\{e\\}$ (even if $B$ is sat
urated).\nThe reduction of $B$ to $H\,$ $B_H:=\\{B_t\\}_{t\\in H}\,$ is a
Fell bundle and one has induction processes $U\\mapsto Ind_{H\\uparrow G}(
U)$ and $T\\mapsto Ind_{B_H\\uparrow B}(T)\,$ where $U$ and $T$ stand for
representations of $H$ and $B_H\,$ respectively. In this talk we use $U\\m
apsto Ind_{H\\uparrow G}(U)$ and $T\\mapsto Ind_{B_H\\uparrow B}(T)$ to co
nstruct two candidates for the "reduced $H$-cross-sectional C*-algebra of
$B$". We also give conditions implying they are isomorphic.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/150/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matt McBride (Mississippi State University)
DTSTART:20240131T200000Z
DTEND:20240131T210000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/151
DESCRIPTION:Title: Crossed Product C*-algebras Associated with p-Adic Multiplication
\nby Matt McBride (Mississippi State University) as part of Noncommuta
tive geometry in NYC\n\n\nAbstract\nI will discuss some basics of p-adic n
umbers\, some examples of $C^*$-algebras that naturally arise from the cro
ssed product of the continuous functions on $Z_p$ with automorphisms and e
ndomorphisms coming from the action of p-adic multiplication. I will also
discuss some basic structure\, including identifying ideals\, short exact
sequences and if time allows some K-Theory.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/151/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Erik Christensen (University of Copenhagen)
DTSTART:20240214T200000Z
DTEND:20240214T210000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/152
DESCRIPTION:Title: From spectral triples in NCG to Grothendieck's inequalities in th
e theory of finite rank matrices\nby Erik Christensen (University of C
openhagen) as part of Noncommutative geometry in NYC\n\n\nAbstract\nWhile
studying properties of a spectral triple\, I realized that the Schur produ
ct - or entry wise product of infinite matrices -- has a nice Stinesprin
g representation as a completely bounded bilinear operator. On the other h
and it is well known that Grothendieck's inequality on bilinear forms has
a dual counterpart\, which describes certain properties of Schur multiplie
rs. It turned out that the theory of operator spaces and completely bounde
d multilinear maps form a nice background to present some classical and so
me new results on both the Schur product and on Grothendieck's inequalitie
s. Part of this will be extended to the non commutative Grothendieck inequ
ality too.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/152/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jacek Krajczok (Vrije Universiteit Brussel)
DTSTART:20240228T200000Z
DTEND:20240228T210000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/153
DESCRIPTION:Title: Approximation properties of discrete quantum groups\nby Jacek
Krajczok (Vrije Universiteit Brussel) as part of Noncommutative geometry
in NYC\n\n\nAbstract\nIt is a classical result in abstract harmonic analys
is\, that discrete group G is amenable if and only if its group von Neuman
n algebra vN(G) has weak* CPAP (completely positive approximation property
). There is also a variant of this result for weak amenability: G is weakl
y amenable if and only if vN(G) has weak* CBAP (completely bounded approxi
mation property). These equivalences remain true also for unimodular discr
ete quantum groups\, which form a class of objects strictly containing dis
crete groups. It is however an open question\, whether approximation prope
rties of vN(G) imply analogous one for G\, if G is a non-unimodular quantu
m group. During the talk I will discuss how one can obtain positive result
s by considering vN(G) not just as a von Neumann algebra\, but as an opera
tor module over $L^1(\\hat{G})$. If time permits\, I will also discuss a r
ecent result about multiplicativity of Cowling-Haagerup (weak amenability)
constant.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/153/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matt McBride (Mississippi State University)
DTSTART:20240327T190000Z
DTEND:20240327T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/154
DESCRIPTION:Title: Derivations on Smooth Subalgebras\nby Matt McBride (Mississip
pi State University) as part of Noncommutative geometry in NYC\n\n\nAbstra
ct\nI will discuss some basics about smooth subalgebras in various algebra
s including the Toeplitz algebra and the Hensel-Steinitz algebra. I will
also discuss classifying derivations on those smooth algebras.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/154/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ilnur Baibulov (St Petersburg State University)
DTSTART:20240221T200000Z
DTEND:20240221T210000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/155
DESCRIPTION:Title: The spectrum of the C*-algebra of singular integral operators wit
h semi-almost periodic coefficients\nby Ilnur Baibulov (St Petersburg
State University) as part of Noncommutative geometry in NYC\n\n\nAbstract\
nThe $C^*$-algebra generated by one-dimensional singular integral operator
s in $L_2(\\mathbb{R})$ is studied. The coefficients are assumed to be con
tinuous and stabilizing at infinity to almost periodic functions. In this
talk I will describe the primitive spectrum of this algebra. The talk is b
ased on collaborative work with O.V. Sarafanov.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/155/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hannes Thiel (Chalmers University of Technology and University of
Gothenburg)
DTSTART:20240313T190000Z
DTEND:20240313T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/156
DESCRIPTION:Title: A gentle introduction to Cuntz semigroups\, I\nby Hannes Thie
l (Chalmers University of Technology and University of Gothenburg) as part
of Noncommutative geometry in NYC\n\n\nAbstract\nThe Cuntz semigroup is a
geometric refinement of K-theory that was\nintroduced by Cuntz in the 197
0s in his pioneering work on the structure\nof simple C*-algebras. This po
werful invariant has seen many\napplications in the structure and classifi
cation theory of C*-algebras.\nRecently\, it has also become clear that Cu
ntz semigroups are interesting\nobjects of study in their own right.\n\nIn
these lectures\, I will give a short introduction to Cuntz semigroups\,\n
and present some examples and applications.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/156/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hannes Thiel (Chalmers University of Technology and University of
Gothenburg)
DTSTART:20240320T190000Z
DTEND:20240320T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/157
DESCRIPTION:Title: A gentle introduction to Cuntz semigroups\, II\nby Hannes Thi
el (Chalmers University of Technology and University of Gothenburg) as par
t of Noncommutative geometry in NYC\n\n\nAbstract\nThe Cuntz semigroup is
a geometric refinement of K-theory that was\nintroduced by Cuntz in the 19
70s in his pioneering work on the structure\nof simple C*-algebras. This p
owerful invariant has seen many\napplications in the structure and classif
ication theory of C*-algebras.\nRecently\, it has also become clear that C
untz semigroups are interesting\nobjects of study in their own right.\n\nI
n these lectures\, I will give a short introduction to Cuntz semigroups\,\
nand present some examples and applications.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/157/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jesús A. Álvarez López (University of Santiago de Compostela)
DTSTART:20240306T200000Z
DTEND:20240306T210000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/158
DESCRIPTION:Title: A trace formula for foliated flows\nby Jesús A. Álvarez Ló
pez (University of Santiago de Compostela) as part of Noncommutative geome
try in NYC\n\n\nAbstract\nIn the lecture\, I will try to explain the ideas
of a recent paper on the trace formula for foliated flows\, written in co
llaboration with Yuri Kordyukov and Eric Leichtnam. Let $\\mathcal{F}$ be
a transversely oriented foliation of codimension one on a closed manifold
$M$\, and let $\\phi=\\{\\phi^t\\}$ be a foliated flow on $(M\,\\mathcal{F
})$ (it maps leaves to leaves). Assume the closed orbits of $\\phi$ are si
mple and its preserved leaves are transversely simple. In this case\, ther
e are finitely many preserved leaves\, which are compact. Let $M^0$ denote
their union\, $M^1=M\\setminus M^0$ and $\\mathcal{F}^1=\\mathcal{F}|_{M^
1}$. We consider two locally convex Hausdorff spaces\, $I(\\mathcal{F})$ a
nd $I'(\\mathcal{F})$\, consisting of the leafwise currents on $M$ that ar
e conormal and dual-conormal to $M^0$\, respectively. They become topologi
cal complexes with the differential operator $d_{\\mathcal{F}}$ induced by
the de~Rham derivative on the leaves\, and they have an $\\mathbb{R}$-act
ion $\\phi^*=\\{\\phi^{t\\\,*}\\}$ induced by $\\phi$. Let $\\bar H^\\bull
et I(\\mathcal{F})$ and $\\bar H^\\bullet I'(\\mathcal{F})$ denote the cor
responding leafwise reduced cohomologies\, with the induced $\\mathbb{R}$-
action $\\phi^*=\\{\\phi^{t\\\,*}\\}$. $\\bar H^\\bullet I(\\mathcal{F})$
and $\\bar H^\\bullet I'(\\mathcal{F})$ are shown to be the central terms
of short exact sequences in the category of continuous linear maps between
locally convex spaces\, where the other terms are described using Witten'
s perturbations of the de~Rham complex on $M^0$ and leafwise Witten's pert
urbations for $\\mathcal{F}^1$. This is used to define some kind of Lefsch
etz distribution $L_{\\rm dis}(\\phi)$ of the actions $\\phi^*$ on both $\
\bar H^\\bullet I(\\mathcal{F})$ and $\\bar H^\\bullet I'(\\mathcal{F})$\,
whose value is a distribution on $\\mathbb{R}$. Its definition involves s
everal renormalization procedures\, the main one is the b-trace of some sm
oothing b-pseudodifferential operator on the compact manifold with boundar
y obtained by cutting $M$ along $M^0$. We also prove a trace formula descr
ibing $L_{\\rm dis}(\\phi)$ in terms of infinitesimal data from the closed
orbits and preserved leaves. Some term of the formula is related with Con
nes' Non-Commutative Geometry of foliations with a transverse measure. Thi
s solves a conjecture of C. Deninger involving two leafwise reduced cohomo
logies instead of a single one.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/158/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gisela Tartaglia (Universidad Nacional de La Plata)
DTSTART:20240403T190000Z
DTEND:20240403T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/159
DESCRIPTION:Title: Induction of coactions for algebraic quantum groups\nby Gisel
a Tartaglia (Universidad Nacional de La Plata) as part of Noncommutative g
eometry in NYC\n\n\nAbstract\nGiven G a discrete group and H a subgroup\,
it is known how to\ninduce G-algebras from H-algebras. In this talk\, we w
ill present a\ngeneralization of this construction in terms of coactions o
f algebraic\nquantum groups. We will start by recalling the basic definiti
ons of\nalgebraic quantum groups\, comodule algebras and cotensor product.
Given\nan a.q.g. A\, we will show how to obtain an A-comodule algebra sta
rting\nfrom a B-comodule algebra\, where B is a compact quantum subgroup o
f A.\nFinally\, we will prove that under some hypothesis\, we obtain a Mor
ita\nequivalence between the crossed products of the corresponding dual\na
ctions.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/159/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter Hochs (Radboud University)
DTSTART:20240424T190000Z
DTEND:20240424T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/160
DESCRIPTION:Title: The equivariant Fried conjecture for suspension flow\nby Pete
r Hochs (Radboud University) as part of Noncommutative geometry in NYC\n\n
\nAbstract\nRay-Singer analytic torsion is a topological invariant of comp
act manifolds\, which can be used to distinguish between homotopy equivale
nt manifolds that are not homeomorphic. The Ruelle dynamical zeta function
is a property of flows on compact manifolds\, which encodes information o
n periodic flow curves. Interestingly\, the absolute value of this functio
n at zero is often equal to the analytic torsion of the manifold\, even th
ough the latter does not involve the flow at all. Fried’s conjecture is
the problem to determine when this equality holds. With Saratchandran\, we
constructed equivariant versions of analytic torsion and the Ruelle zeta
function for proper group actions\, and posed the question when an equivar
iant version of Fried’s conjecture holds. With Pirie\, we are investigat
ing this conjecture for a specific type of flows: suspension flows of diff
eomorphisms.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/160/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tatiana Shulman (University of Gothenburg)
DTSTART:20240410T190000Z
DTEND:20240410T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/161
DESCRIPTION:Title: On almost commuting matrices\nby Tatiana Shulman (University
of Gothenburg) as part of Noncommutative geometry in NYC\n\n\nAbstract\nQu
estions of whether almost commuting matrices are necessarily close to comm
uting ones are old. They are reformulated using $C^*$-algebra theory and h
ave somewhat topological nature. We investigate which relations for famili
es of commuting matrices are stable under small perturbations and give som
e applications. Joint work with Dominic Enders.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/161/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mitch Hamidi (Embry‑Riddle Aeronautical University)
DTSTART:20240417T190000Z
DTEND:20240417T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/162
DESCRIPTION:Title: $C^*$-extensions of non-self-adjoint dynamics\nby Mitch Hamid
i (Embry‑Riddle Aeronautical University) as part of Noncommutative geome
try in NYC\n\n\nAbstract\nGiven the action of a group G on a non-self-adjo
int operator algebra A\, the crossed product of A by G can be realized as
the subalgebra of a $C^*$-crossed product when the dynamics of G acting on
A can be extended to self-adjoint dynamics of G acting on a $C^*$-algebra
. In this talk\, we characterize the existence of such a dynamical extensi
on in terms of the boundary ideal structure for A in its maximal represent
ation. We define a lattice structure for an operator algebra’s completel
y isometric representation theory and discuss how one might recover the cr
ossed product of an operator algebra in a representation lacking a self-ad
joint dynamical extension.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/162/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Changying Ding (UCLA)
DTSTART:20240501T190000Z
DTEND:20240501T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/163
DESCRIPTION:Title: On Cartan subalgebras of $II_1$ factors arising from Bernoulli ac
tions of weakly amenable groups\nby Changying Ding (UCLA) as part of N
oncommutative geometry in NYC\n\n\nAbstract\nA conjecture of Popa states t
hat the $II_1$ factor arising from a Bernoulli action of a nonamenable gro
up has a unique (group measure space) Cartan subalgebra\, up to unitary co
njugacy. In this talk\, I will discuss this conjecture and show that it ho
lds for weakly amenable groups with constant $1$ among algebraic actions.
The proof involves the notion of properly proximal groups introduced by Bo
utonnet\, Ioana\, and Peterson.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/163/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ralf Meyer (Georg-August-Universität Göttingen)
DTSTART:20240529T190000Z
DTEND:20240529T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/164
DESCRIPTION:Title: Classification of Purely Infinite Graph C*-Algebras\nby Ralf
Meyer (Georg-August-Universität Göttingen) as part of Noncommutative geo
metry in NYC\n\n\nAbstract\nI will explain how purely infinite graph $C^*$
-algebras may be classified up to stable isomorphism using an invariant of
K-theoretic nature. This is contained in my recent preprint with Rasmus
Bentmann. The key idea is to classify $C^*$-correspondences from a graph
$C^*$-algebra to another $C^*$-algebra up to homotopy\, using some project
ions and unitaries in the target $C^*$-algebra. Since we classify corresp
ondences up to homotopy\, we also classify general graph $C^*$-algebras up
to homotopy equivalence. The relevant homotopies will automatically pres
erve gauge-invariant ideals\, and we may improve this to also preserve the
ideals that are not gauge invariant\, if these are present.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/164/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alcides Buss (Federal University of Santa Catarina\, Brazil)
DTSTART:20240911T190000Z
DTEND:20240911T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/165
DESCRIPTION:Title: P-adic Operator Algebras\nby Alcides Buss (Federal University
of Santa Catarina\, Brazil) as part of Noncommutative geometry in NYC\n\n
\nAbstract\nIn this talk we present the of p-adic operator algebras\, whic
h are nonarchimedean analogues of $C^*$-algebras. We demonstrate that vari
ous classical examples of operator algebras - such as group(oid) algebras
- have a nonarchimedean counterpart. The category of p-adic operator algeb
ras exhibits a similar flavor to the category of real and complex $C^*$-al
gebras\, featuring limits\, colimits\, tensor products\, crossed products
and an enveloping construction permitting us to construct p-adic operator
algebras from involutive algebras over $Z_p$. Finally\, we briefly discuss
an analogue of topological K-theory for Banach $Z_p$-algebras\, and compu
te it in basic examples\, like Cuntz algebras and rotation algebras.\n\nTh
is is joint work with Luiz Felipe Garcia and Devarshi Mukherjee.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/165/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bojan Kuzma (University of Primorska\, Slovenia)
DTSTART:20240918T190000Z
DTEND:20240918T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/167
DESCRIPTION:Title: Birkhoff-James orthogonality in normed vector spaces\nby Boja
n Kuzma (University of Primorska\, Slovenia) as part of Noncommutative geo
metry in NYC\n\n\nAbstract\nBirkhoff-James orthogonality generalizes the c
lassical orthogonality from Hilbert to general normed spaces. It can be a
useful tool for finding the best approximation of a vector within a given
subspace. However\, unlike the classical one\, it is in general not sym
metric. In fact (in dimensions greater than 2) it is symmetric if and only
if the norm is induced by the inner product. This early classification of
inner-product spaces goes back to James (for real Banach spaces) with an
aid of Bohnenblust (for complex ones). One can visualize this relation as
an infinite directed graph (called ortho-digraph)\, where vertices are a
ll the vectors from a normed space (or all points in its projectivisation)
and two vertices x\, y form a directed edge if x is Birkhoff-James ortho
gonal to y .We will show that this digraph contains a lot of information a
bout the normed space: It knows how to calculate the dimension of the unde
rlying space\, knows if the norm is rotund or smooth\, knows how to find s
mooth points and in some special cases even knows if the underlying field
is real or complex. At least for smooth spaces in can even completely char
acterize them\, modulo (conjugate) linear isometry.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/167/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bora Yalkinoglu (Université de Strasbourg\, CNRS)
DTSTART:20240925T190000Z
DTEND:20240925T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/168
DESCRIPTION:Title: On the discrete periodic Toda flow\nby Bora Yalkinoglu (Unive
rsité de Strasbourg\, CNRS) as part of Noncommutative geometry in NYC\n\n
\nAbstract\nThe discrete periodic Toda flow is a very interesting integrab
le system. The goal of our talk is to explain how it can be linearized in
terms of Gauß composition law for quadratic forms. \nFurther\, we will in
dicate how the periodic box-ball flow\, a famous tropical integrable syste
m\,\ncan naturally be embedded into the Toda system and from there point t
o some intriguing relations with number theory.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/168/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Valerio Proietti (University of Oslo)
DTSTART:20241002T190000Z
DTEND:20241002T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/169
DESCRIPTION:Title: Elliott invariant in a geometric context\nby Valerio Proietti
(University of Oslo) as part of Noncommutative geometry in NYC\n\n\nAbstr
act\nGiven a class of topological dynamical systems\, we study the associa
ted mapping torus from the point of view of foliated spaces. By studying t
he interaction between the leafwise Dirac operator and the invariant trans
verse measures\, we reframe in a geometric fashion the Elliott invariant f
or the crossed product of the dynamical system\, and prove a rigidity resu
lt for the mapping torus\, lifting leafwise homotopy equivalences to isomo
rphism of the noncommutative leaf space. Joint work with Hao Guo and Hang
Wang.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/169/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alistair Miller (University of Southern Denmark)
DTSTART:20241009T190000Z
DTEND:20241009T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/170
DESCRIPTION:Title: Homology and K-theory for self-similar group actions\nby Alis
tair Miller (University of Southern Denmark) as part of Noncommutative geo
metry in NYC\n\n\nAbstract\nSelf-similar groups are groups of automorphism
s of infinite rooted trees obeying a simple but powerful rule. Under this
rule\, groups with exotic properties can be generated from very basic star
ting data\, most famously the Grigorchuk group which was the first example
of a group with intermediate growth.\n\nNekrashevych introduced a groupoi
d and a $C^*$-algebra for a self-similar group action on a tree as models
for some underlying noncommutative space for the system. Our goal is to co
mpute the K-theory of the $C^*$-algebra and the homology of the groupoid.
Our main theorem provides long exact sequences which reduce the problems t
o group theory. I will demonstrate how to apply this theorem to fully comp
ute homology and K-theory through the example of the Grigorchuk group.\n\n
This is joint work with Benjamin Steinberg.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/170/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robert Yuncken (Université de Lorraine)
DTSTART:20250129T200000Z
DTEND:20250129T210000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/171
DESCRIPTION:Title: Crystallizing the algebra of functions on a compact semisimple Li
e group\nby Robert Yuncken (Université de Lorraine) as part of Noncom
mutative geometry in NYC\n\n\nAbstract\nThe theory of crystal bases is a m
eans of simplifying the representation theory of semisimple Lie algebras b
y passing through quantum groups. Varying the parameter q of the quantize
d enveloping algebras\, we pass from the classical theory at q=1 through t
he Drinfeld-Jimbo algebras at 0 < q < 1 to the crystal limit at q=0. At t
his point\, the main features of the representation theory crystallize int
o purely combinatorial data described by crystal graphs. In this talk\, w
e will describe what happens to the algebra of continuous functions on a c
ompact semisimple Lie group under the crystallization process\, yielding h
igher-rank graph algebras. This is joint work with Marco Matassa.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/171/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Isaac Goldbring (University of California\, Irvine)
DTSTART:20241016T190000Z
DTEND:20241016T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/172
DESCRIPTION:Title: What is…model theory of operator algebras?\nby Isaac Goldbr
ing (University of California\, Irvine) as part of Noncommutative geometry
in NYC\n\n\nAbstract\nModel theory is the area of logic that studies math
ematical structures through the lens of first-order logic\, examining what
properties of a structure are expressible by first-order sentences and an
alyzing what subsets of the structure can be defined using first-order for
mulae. In the last 15 years or so\, the model theory of operator algebras
has been a very active field with exciting interactions taking place betw
een the model theoretic and operator algebraic communities. In this talk\
, I will survey some of the main themes being pursued in the model theory
of tracial von Neumann algebras. No prior knowledge of logic or model the
ory will be assumed.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/172/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniela Di Donato (University of Pavia)
DTSTART:20241023T190000Z
DTEND:20241023T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/173
DESCRIPTION:Title: Rectifiability in Carnot groups\nby Daniela Di Donato (Univer
sity of Pavia) as part of Noncommutative geometry in NYC\n\n\nAbstract\nIn
trinsic regular surfaces in Carnot groups play the same role as $C^1$ surf
aces in Euclidean spaces. As in Euclidean spaces\, intrinsic regular surfa
ces can be locally defined in different ways: e.g. as non critical level s
ets or as continuously intrinsic differentiable graphs. The equivalence of
these natural definitions is the problem that we are studying. Precisely
our aim is to generalize some results proved by Ambrosio\, Serra Cassano\,
Vittone valid in Heisenberg groups to the more general setting of Carnot
groups. This is joint work with Antonelli\, Don and Le Donne\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/173/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jintao Deng (SUNY at Buffalo)
DTSTART:20241030T190000Z
DTEND:20241030T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/174
DESCRIPTION:Title: Twisted Roe Algebras and the Coarse Baum-Connes Conjecture\nb
y Jintao Deng (SUNY at Buffalo) as part of Noncommutative geometry in NYC\
n\n\nAbstract\nThe coarse Baum-Connes conjecture claims that certain topol
ogical K-homology and the K-theory of Roe algebras associated to metric sp
aces are isomorphic via the index map. It provides algorithm to compute th
e higher indices for elliptic operators on non-compact Riemannian manifold
s. The higher index is an element of the K-theory of the Roe algebra. To
understand Roe algebras\, we introduced a notion of twisted Roe algebras a
nd a twisted coarse Baum-Connes conjecture. In the talk\, I will cover bas
ic properties of the twisted Roe algebras and the K-theory for the twisted
algebras associated with metric spaces with a coarsely embeddable fibrati
on structure. As an application\, the coarse Baum-Connes conjecture holds
for a finitely generated group which is an extension of coarsely embeddabl
e groups. This is based on a joint work with Liang Guo.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/174/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Meenakshi McNamara (Perimeter Institute)
DTSTART:20241127T210000Z
DTEND:20241127T220000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/175
DESCRIPTION:Title: The exact quantum chromatic number of Hadamard graphs and their p
roducts\nby Meenakshi McNamara (Perimeter Institute) as part of Noncom
mutative geometry in NYC\n\n\nAbstract\nQuantum chromatic numbers are defi
ned via non-local games on classical graphs. Very few exact computations o
f the quantum chromatic number of graphs are known. In this talk\, we will
give a proof of the exact quantum chromatic number of Hadamard graphs. As
opposed to prior results on this problem\, this approach uses results on
conjugacy class graphs which allows us to consider products of Hadamard gr
aphs as well. Specifically\, we compute the exact quantum chromatic number
of categorical products of Hadamard graphs.\n\nThroughout this work\, we
use several results for the quantum chromatic numbers of quantum graphs\,
an operator algebraic generalization of classical graphs that appears in c
onnection to quantum information theory. In particular\, we also discuss r
esults on products of quantum graphs appearing in joint work with Rolando
de Santiago.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/175/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eduardo Scarparo (Federal University of Pelotas\, Brazil)
DTSTART:20250205T200000Z
DTEND:20250205T210000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/176
DESCRIPTION:Title: A tracial characterization of Furstenberg's x p\, x q conjecture<
/a>\nby Eduardo Scarparo (Federal University of Pelotas\, Brazil) as part
of Noncommutative geometry in NYC\n\n\nAbstract\nFurstenberg's conjecture
about xp\, xq\, invariant measures on $[0\,1)$\, where p and q are multipl
icatively independent integers\, is one of the most fundamental open probl
ems in ergodic theory. We will see how the topological counterpart of this
conjecture\, which is a theorem due to Furstenberg\, implies the uniquene
ss of the $C^*$-norm on the complex group ring of a certain metabelian gro
up $G$.\n\nFurthermore\, we will present a characterization of the xp\,xq
conjecture in terms of the traces of $C^*(G)$\, and discuss the primitive
ideal space and K-theory of $C^*(G)$. This is based on joint work with Chr
is Bruce.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/176/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Isaac Goldbring (University of California\, Irvine)
DTSTART:20250507T190000Z
DTEND:20250507T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/177
DESCRIPTION:Title: Minicourse: Applications of model theory to operator algebras\, I
\nby Isaac Goldbring (University of California\, Irvine) as part of No
ncommutative geometry in NYC\n\n\nAbstract\nIn these three talks\, I will
outline several applications of model theory to operator algebras. In the
first talk\, I will explain how model theory sheds light on the recent re
solution of the Connes Embedding Problem from the quantum complexity resul
t known as MIP*=RE. In the second talk\, I will explain how the ideas fro
m the first talk also give information about the class of QWEP C*-algebras
introduced by Kirchberg in the 1990s. In the final talk\, I will discuss
two problems centered around relative commutants of tracial von Neumann a
lgebras in ultrapowers and how they are intimately connected with model th
eoretic ideas. These talks will be independent of each other and from the
talk I gave in this seminar in the fall.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/177/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Isaac Goldbring (University of California\, Irvine)
DTSTART:20250514T190000Z
DTEND:20250514T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/178
DESCRIPTION:Title: Minicourse: Applications of model theory to operator algebras\,
II\nby Isaac Goldbring (University of California\, Irvine) as part of
Noncommutative geometry in NYC\n\n\nAbstract\nIn these three talks\, I wil
l outline several applications of model theory to operator algebras. In t
he first talk\, I will explain how model theory sheds light on the recent
resolution of the Connes Embedding Problem from the quantum complexity res
ult known as MIP*=RE. In the second talk\, I will explain how the ideas f
rom the first talk also give information about the class of QWEP C*-algebr
as introduced by Kirchberg in the 1990s. In the final talk\, I will discu
ss two problems centered around relative commutants of tracial von Neumann
algebras in ultrapowers and how they are intimately connected with model
theoretic ideas. These talks will be independent of each other and from t
he talk I gave in this seminar in the fall.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/178/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Isaac Goldbring (University of California\, Irvine)
DTSTART:20250521T190000Z
DTEND:20250521T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/179
DESCRIPTION:Title: Minicourse: Applications of model theory to operator algebras\, I
II\nby Isaac Goldbring (University of California\, Irvine) as part of
Noncommutative geometry in NYC\n\n\nAbstract\nIn these three talks\, I wil
l outline several applications of model theory to operator algebras. In t
he first talk\, I will explain how model theory sheds light on the recent
resolution of the Connes Embedding Problem from the quantum complexity res
ult known as MIP*=RE. In the second talk\, I will explain how the ideas f
rom the first talk also give information about the class of QWEP C*-algebr
as introduced by Kirchberg in the 1990s. In the final talk\, I will discu
ss two problems centered around relative commutants of tracial von Neumann
algebras in ultrapowers and how they are intimately connected with model
theoretic ideas. These talks will be independent of each other and from t
he talk I gave in this seminar in the fall.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/179/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Raphael Ponge (Sichuan University)
DTSTART:20241106T200000Z
DTEND:20241106T210000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/180
DESCRIPTION:Title: Noncommutative geometry and semiclassical analysis\nby Raphae
l Ponge (Sichuan University) as part of Noncommutative geometry in NYC\n\n
\nAbstract\nIn this talk\, I will present new results regarding semiclassi
cal Weyl’s laws in the setup of Connes’ noncommutative geometry. They
provide precise asymptotics for the counting functions of Schroedinger ope
rators under the semiclassical limit. This improves and simplifies previou
s results of McDonald-Sukochev-Zanin. This provides a bridge between semic
lassical analysis and noncommutative geometry. Thanks to the Birman-Scwhin
ger principle and old results of Birman-Solomyak this reduces to establish
ing various weak Schatten class properties for the operators at stake. Thi
s has a number of applications. We shall present two of them. First\, we r
ecover previously known semiclassical Weyl’s laws on Euclidean domains a
nd closed manifolds. These results were proved in 60s and 70s. However\,
thanks to our setup\, they can be deduced results of Minakshisundaram and
Pleijel on short time heat kernel asymptotics for Laplacians that were est
ablished in the late 40s. Second\, we obtain semiclassical Weyl laws for n
oncommutative tori for any dimension. These laws were conjectured by Ed Mc
Donald and the speaker.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/180/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shuoxing Zhou (École Normale Supérieure)
DTSTART:20241113T200000Z
DTEND:20241113T210000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/181
DESCRIPTION:Title: Noncommutative topological boundaries and amenable invariant inte
rmediate subalgebras\nby Shuoxing Zhou (École Normale Supérieure) as
part of Noncommutative geometry in NYC\n\n\nAbstract\nAs an analogue of t
he topological boundary of discrete groups $\\Gamma$\, we define the nonco
mmutative topological boundary of tracial von Neumann algebras $(M\,\\tau)
$ and apply it to generalize a recent result by Amrutam-Hartman-Oppelmayer
\, showing that for a trace preserving action $\\Gamma \\curvearrowright (
A\,\\tau_A)$ on an amenable tracial von Neumann algebra\, any $\\Gamma$-in
variant amenable intermediate subalgebra between $A$ and $\\Gamma\\ltimes
A$ is necessarily a subalgebra of $\\mathrm{Rad}(\\Gamma) \\ltimes A$. By
taking $(A\,\\tau_A)=L^\\infty(X\,\\nu_X)$ for a free pmp action $\\Gamma
\\curvearrowright (X\,\\nu_X)$\, we obtain a similar result for invariant
subequivalence relations of $\\mathcal{R}_{\\Gamma \\curvearrowright X}$.\
n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/181/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aaron Kettner (Czech Academy of Sciences)
DTSTART:20241204T200000Z
DTEND:20241204T210000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/182
DESCRIPTION:Title: Cuntz–Pimsner algebras of twisted partial automorphisms\nby
Aaron Kettner (Czech Academy of Sciences) as part of Noncommutative geome
try in NYC\n\n\nAbstract\nWe will discuss how to construct a $C^*$-algebra
from a vector bundle\nand a partial action of the integers on the base sp
ace of the bundle\,\nusing the machinery of Cuntz–Pimsner algebras. Desp
ite being much more\ngeneral\, the resulting algebras share many propertie
s with partial\ncrossed products by the integers. They also generalise the
\n$C^*$-algebras constructed from homeomorphisms twisted by vector bundles
\nrecently introduced by\nAdamo–Archey–Forough–Georgescu–Jeong–S
trung–Viola. Under natural\nconditions on the action and the space\, cla
ssifiability of the\n$C^*$-algebras is shown. In particular\, we obtain bo
th stably finite as\nwell as purely infinite classifiable $C^*$-algebras f
rom the same\ndynamical framework.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/182/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Damien Tageddine (McGill University)
DTSTART:20241211T200000Z
DTEND:20241211T210000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/183
DESCRIPTION:Title: Noncommutative geometry on the Berkovich projective line\nby
Damien Tageddine (McGill University) as part of Noncommutative geometry in
NYC\n\n\nAbstract\nThe Berkovich projective line is an analytic space ove
r a non-Archimedean field. It can also be constructed as an inverse limit
of finite rooted trees. \nWe find how to associate $C^*$-algebras generate
d by partial isometries to the Berkovich line. This allows us to construct
several spectral triples on this space. \nFinally\, we show that invarian
t measures\, such as the Patterson-Sullivan measure\, can be obtained as c
ertain KMS-states of the crossed product algebra with a subgroup of $PGL_2
(C_p)$.\n\nThis is a joint work with Masoud Khalkhali.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/183/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jun Yang (Harvard)
DTSTART:20250212T200000Z
DTEND:20250212T210000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/184
DESCRIPTION:Title: The Jacquet-Langlands correspondence of von Neumann dimensions ov
er arithmetic groups\nby Jun Yang (Harvard) as part of Noncommutative
geometry in NYC\n\n\nAbstract\nWe first show the local-global compatibilit
y of Tamagawa measures and Plancherel measures under the local/global Jacq
uet-Langlands correspondence. We then prove that the global Jacquet-Langla
nds correspondence preserves von Neumann dimensions over arithmetic groups
.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/184/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Noemie Combe (University of Warsaw)
DTSTART:20250219T200000Z
DTEND:20250219T210000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/185
DESCRIPTION:Title: Quantum Information Geometry and the Connes–Araki–Haagerup Co
nes\nby Noemie Combe (University of Warsaw) as part of Noncommutative
geometry in NYC\n\n\nAbstract\nThe profound interplay between von Neumann
algebras and quantum field theory has increasingly highlighted their impor
tance in higher category theory and topology. A central insight emerges fr
om Tomita–Takesaki theory\, which studies the modular automorphism group
s of von Neumann algebras. Using techniques from affine differential geome
try\, we establish an explicit connection between the Connes–Araki–Haa
gerup cones—objects invariant under modular operators—and geometric st
ructures intrinsic to the axiomatization of 2D topological quantum field t
heory (TQFT).\n\nWe demonstrate that these strictly convex symmetric cones
possess a pre-Frobenius structure and contain a submanifold satisfying th
e Witten–Dijkgraaf–Verlinde–Verlinde (WDVV) equation\, thereby formi
ng a Frobenius submanifold. This result reveals new and concrete relations
hips between objects invariant under modular operators and low-dimensional
TQFTs\, with additional implications for quantum information geometry.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/185/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gabor Etesi (Budapest University of Technology and Economics)
DTSTART:20250312T190000Z
DTEND:20250312T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/186
DESCRIPTION:Title: The four dimensional smooth Poincare conjecture from the viewpoin
t of Neumann algebra representations\nby Gabor Etesi (Budapest Univers
ity of Technology and Economics) as part of Noncommutative geometry in NYC
\n\n\nAbstract\nIn this talk we outline the construction and basic propert
ies of\na new smooth 4-manifold invariant obtained by the aid of the rich\
nrepresentation theory of the hyperfinite II_1 factor von Neumann algebra.
\nThis invariant gives rise to a unital Abelian semigroup homomorphism fro
m\n(the category of) connected compact oriented smooth 4-manifold equipped
\nwith the connected sum operation into the semi-open interval [0\,1) with
\nAbelian semigroup operation $(s\,t)\\mapsto s+t-st$. This invariant has
the\ninteresting property that its range is appropriately restricted by th
e\npossible values of Jones' indices of subfactors within the II_1\nhyperf
inite factor hence consists of a discrete and a continuous part. It\nis th
en observed that (i) the invariant is not injective on its continuous\nran
ge part\; (ii) when evaluated on the standard 4-sphere its value falls\nwi
thin the discrete part of the range and its injectivity at this specific\n
value is equivalent to the validity of the 4 dimensional smooth Poincare\n
conjecture. Moreover\, as the punch line of this talk\, it is expected tha
t\nthis invariant possesses a sort of continuity hence non-invertability a
t\nits specifec values in the continuous range will imply non-invartabilit
y\nat nearby values\; however such argument cannot be applied to study the
4\ndimensional smooth Poincare conjecture because of the aforementioned\n
discreteness hence the conjecture's difficulty might be related with\nthe
isolation of the 4-sphere in this sense from the rest of smooth\n4-manifol
ds.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/186/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuri Bazlov (University of Manchester)
DTSTART:20250226T200000Z
DTEND:20250226T210000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/187
DESCRIPTION:Title: Cocycle twists of algebras\, representations and orders\nby Y
uri Bazlov (University of Manchester) as part of Noncommutative geometry i
n NYC\n\n\nAbstract\nA way to deform an associative algebra $A$ is to twis
t the\nmultiplication by a 2-cocycle on a group or a Hopf algebra acting o
n\n$A$. I am interested to know to what extent the representations (and\nr
ing-theoretic and homological properties) of the twist are determined\nby
those of $A$. My case in point will be rational Cherednik algebras\nover c
omplex reflection groups: twists of these well-studied objects\ngive algeb
ras\, with similar PBW bases\, over "mystic reflection groups"\,\nand for
some of them we can give an explicit combinatorial description\nof standar
d modules(arXiv:2501.06673\, with Jones-Healey). Twists\ndescend to finite
-dimensional quotients of Cherednik algebras at $t=0$\,\nand over number f
ields\, seem to produce their forms (in the sense that\nthe twist triviali
zes over a field extension). This hints at an\ninterplay between twists an
d arithmetic\; if time permits\, I will mention\na possible connection to
Hopf-Galois structures on fields.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/187/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chris Bruce (Newcastle University)
DTSTART:20250326T190000Z
DTEND:20250326T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/188
DESCRIPTION:Title: On the C*-algebra of Connes’ adele class space\nby Chris Br
uce (Newcastle University) as part of Noncommutative geometry in NYC\n\n\n
Abstract\nThe multiplicative group of an algebraic number field acts by mu
ltiplication on the adele ring of the field\, and the quotient space for t
his action is Connes’ adele class space. I will give an overview of join
t work with Takuya Takeishi in which we prove that the crossed product $C^
*$-algebra associated with the adele class space completely remembers the
number field. Precisely\, we prove that two such crossed product C*-algebr
as are *-isomorphic if and only if the underlying number fields are isomor
phic. Primitive ideals and subquotients play a central role in our proof.\
n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/188/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Manuel Reyes (University of California\, Irvine)
DTSTART:20250319T190000Z
DTEND:20250319T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/189
DESCRIPTION:Title: Searching for noncommutative spectrum functors\nby Manuel Rey
es (University of California\, Irvine) as part of Noncommutative geometry
in NYC\n\n\nAbstract\nIn the classical algebra-geometry correspondences\,
the assignment turning an algebra into a space is a type of spectrum. Thus
spectra of noncommutative algebras have been of interest for a long time
in both algebra and noncommutative geometry. Because the spectrum typicall
y provides a functor from commutative algebras to spaces\, it is natural t
o ask whether we can extend it to a noncommutative spectrum functor. I wil
l discuss this problem\, along with negative and partial positive results
toward its resolution.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/189/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Pitts (University of Nebraska-Lincoln)
DTSTART:20250416T190000Z
DTEND:20250416T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/190
DESCRIPTION:Title: Pseudo-Cartan Inclusions and their Cartan Envelopes\nby David
Pitts (University of Nebraska-Lincoln) as part of Noncommutative geometry
in NYC\n\n\nAbstract\nI will discuss the class of pseudo-Cartan inclusion
s\,\n which are a class of regular inclusions of $C^*$-algebras\n $\\mat
hcal D\\subseteq \\mathcal C$ where $\\mathcal D$ is abelian.\n This clas
s includes several previously studied classes such as:\n Cartan inclusion
s\, weak Cartan inclusions and virtual Cartan\n inclusions.\n\n The clas
s of pseudo-Cartan inclusions coincides with the class of regular\n inclu
sions having a Cartan envelope. Roughly speaking\, a Cartan\n envelope
for a regular inclusion is a minimal Cartan inclusion into\n which the i
nclusion regularly embeds.\n\n Pseudo-Cartan inclusions and their Cartan
envelopes have desirable\n properties: for example\, they\n behave well
under suitable inductive limits and under minimal tensor\n products.\n \
n Time permitting\, I will describe some applications. Here is a\n samp
le Application: Suppose for $i=1\,2$\,\n $(\\mathcal C_i\,\\mathcal D_i)
$ are pseudo-Cartan inclusions and\n $\\mathcal A_i$ are intermediate Ban
ach algebras\,\n\\[\\mathcal D_i\\subseteq \\mathcal A_i\\subseteq \\mathc
al C_i.\\] If $\\theta: \\mathcal A_1\\rightarrow\n\\mathcal A_2$ is an i
sometric isomorphism\, then $\\theta$ uniquely extends to a\n$*$-isomorphi
sm of the $C^*$-subalgebras of $\\mathcal C_i$ generated by \n$\\mathcal A
_i$\,\n\\[\\tilde\\theta: C^*(\\mathcal A_1)\\rightarrow C^*(\\mathcal A_2
).\\]\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/190/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Frank (HTWK Leipzig)
DTSTART:20250402T190000Z
DTEND:20250402T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/191
DESCRIPTION:Title: Multiplier modules of Hilbert $C^*$-modules revisited\nby Mic
hael Frank (HTWK Leipzig) as part of Noncommutative geometry in NYC\n\n\nA
bstract\nFollowing the approach to multiplier modules of Hilbert $C^*$-mod
ules introduced by D. Bakić and \nB. Guljaš (2003) we reconsider key def
initions and facts to get deeper insights into related structures. The ind
ependent approach by M. Daws (2010) and by A. Buss\, B. Kwaśniewski\, A.
McKee\, A. Skalski (2024) via Banach $C^*$-modules serves as an alternativ
e point of view on which we comment and give facts to interrelate these tw
o theories. \nThe property of a Hilbert $C^*$-module to be a multiplier $C
^*$-module is shown to be an invariant with respect to the consideration a
s a left or right Hilbert C*-module in the sense of a $C^*$-correspondence
in strong Morita equivalence theory. The interrelation of the C*-algebras
of "compact" operators\, the Banach algebras of bounded module operators
and the Banach spaces of bounded module operators of a Hilbert $C^*$-modul
e to its $C^*$-dual Banach $C^*$-module are characterized for pairs of Hil
bert $C^*$-modules and their respective multiplier modules. The structures
on the latter are always isometrically embedded into the respective struc
tures on the former. Examples for which continuation of these kinds of bou
nded module operators from the initial Hilbert $C^*$-module to its multipl
ier module fails are given\, however existing continuations turn out to be
always unique. Similarly\, bounded modular functionals from both kinds of
Hilbert $C^*$-modules to their respective $C^*$-algebras of coefficients
are compared\, and eventually existing continuations are shown to be uniqu
e.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/191/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Itamar Vigdorovich (University of California\, San Diego)
DTSTART:20250409T190000Z
DTEND:20250409T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/192
DESCRIPTION:Title: Structural properties of reduced $C^∗$-algebras associated with
higher-rank lattices\nby Itamar Vigdorovich (University of California
\, San Diego) as part of Noncommutative geometry in NYC\n\n\nAbstract\nWe
present the first examples of higher-rank lattices whose reduced $C^*$-alg
ebras satisfy strict comparison\, stable rank one\, selflessness\, uniquen
ess of embeddings of the Jiang--Su algebra\, and allow explicit computatio
ns of the Cuntz semigroup. This resolves a question raised in recent groun
dbreaking work of Amrutam\, Gao\, Kunnawalkam Elayavalli\, and Patchell\,
in which they exhibited a large class of finitely generated non-amenable g
roups satisfying these properties. Our proof relies on quantitative estima
tes in projective dynamics\, crucially using the exponential mixing for di
agonalizable flows. As a result\, we obtain an effective mixed-identity-fr
eeness property\, which\, combined with V. Lafforgue's rapid decay theorem
\, yields the desired conclusions.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/192/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrei Alpeev (Ecole Normale Supérieure)
DTSTART:20250910T190000Z
DTEND:20250910T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/193
DESCRIPTION:Title: C*-simplicity and the Poisson boundary\nby Andrei Alpeev (Eco
le Normale Supérieure) as part of Noncommutative geometry in NYC\n\n\nAbs
tract\nA connection between the Furstenberg boundary and $C^*$-simplicity
of groups was a major breakthrough of the previous decade by Kalantar and
Kennedy.\nThe furstenberg boundary is a topological object associated with
a group. The Poisson boundary is a measurable object\, associated with a
pair of a group and a probability measure on the group\, that describes th
e asymptotic behaviour of the random walk on the group.\nI will talk about
a connection between $C^*$-simplicity and the Poisson boundary\, namely\,
that a countable group is $C^*$-simple iff its natural action on the Pois
son boundary is essentially free for a generic measure on the group.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/193/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alastair Hamilton (Texas Tech University)
DTSTART:20250917T190000Z
DTEND:20250917T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/194
DESCRIPTION:Title: Noncommutative geometry in effective field theory and large N phe
nomena\nby Alastair Hamilton (Texas Tech University) as part of Noncom
mutative geometry in NYC\n\n\nAbstract\nIn this talk I will discuss the no
tion of an effective field theory\, as formally introduced by Costello\, a
nd its manifestation in the framework of noncommutative geometry introduce
d by Kontsevich. Noncommutative geometry arises within this context from r
eplacing ordinary Feynman diagrams with diagrams of interacting open strin
gs\, and I will explain how the large N phenomena first discovered by ‘t
Hooft arises in this framework. Here a connection can be made between the
se open string type theories that arise in noncommutative geometry and lar
ge N gauge theories using the Loday-Quillen-Tsygan theorem from algebraic
K-theory. If time permits\, I may discuss the treatment of the Batalin-Vil
kovisky formalism within this context and the connection with moduli space
s of Riemann surfaces.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/194/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anne-Marie Aubert (CNRS\, Sorbonne Université - Université de Pa
ris)
DTSTART:20250609T140000Z
DTEND:20250609T150000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/195
DESCRIPTION:Title: NSF-CBMS conference "Representations of p-adic groups and noncomm
utative geometry"\, Lecture 1\nby Anne-Marie Aubert (CNRS\, Sorbonne U
niversité - Université de Paris) as part of Noncommutative geometry in N
YC\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/195/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anne-Marie Aubert (CNRS\, Sorbonne Université - Université de Pa
ris)
DTSTART:20250609T150000Z
DTEND:20250609T160000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/196
DESCRIPTION:Title: NSF-CBMS conference "Representations of p-adic groups and noncomm
utative geometry"\, Lecture 2\nby Anne-Marie Aubert (CNRS\, Sorbonne U
niversité - Université de Paris) as part of Noncommutative geometry in N
YC\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/196/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anne-Marie Aubert (CNRS\, Sorbonne Université - Université de Pa
ris)
DTSTART:20250610T133000Z
DTEND:20250610T143000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/197
DESCRIPTION:Title: NSF-CBMS conference "Representations of p-adic groups and noncomm
utative geometry"\, Lecture 3\nby Anne-Marie Aubert (CNRS\, Sorbonne U
niversité - Université de Paris) as part of Noncommutative geometry in N
YC\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/197/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anne-Marie Aubert (CNRS\, Sorbonne Université - Université de Pa
ris)
DTSTART:20250610T150000Z
DTEND:20250610T160000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/198
DESCRIPTION:Title: NSF-CBMS conference "Representations of p-adic groups and noncomm
utative geometry"\, Lecture 4\nby Anne-Marie Aubert (CNRS\, Sorbonne U
niversité - Université de Paris) as part of Noncommutative geometry in N
YC\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/198/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anne-Marie Aubert (CNRS\, Sorbonne Université - Université de Pa
ris)
DTSTART:20250611T133000Z
DTEND:20250611T143000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/199
DESCRIPTION:Title: NSF-CBMS conference "Representations of p-adic groups and noncomm
utative geometry"\, Lecture 5\nby Anne-Marie Aubert (CNRS\, Sorbonne U
niversité - Université de Paris) as part of Noncommutative geometry in N
YC\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/199/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anne-Marie Aubert (CNRS\, Sorbonne Université - Université de Pa
ris)
DTSTART:20250611T150000Z
DTEND:20250611T160000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/200
DESCRIPTION:Title: NSF-CBMS conference "Representations of p-adic groups and noncomm
utative geometry"\, Lecture 6\nby Anne-Marie Aubert (CNRS\, Sorbonne U
niversité - Université de Paris) as part of Noncommutative geometry in N
YC\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/200/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anne-Marie Aubert (CNRS\, Sorbonne Université - Université de Pa
ris)
DTSTART:20250612T133000Z
DTEND:20250612T143000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/201
DESCRIPTION:Title: NSF-CBMS conference "Representations of p-adic groups and noncomm
utative geometry"\, Lecture 7\nby Anne-Marie Aubert (CNRS\, Sorbonne U
niversité - Université de Paris) as part of Noncommutative geometry in N
YC\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/201/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anne-Marie Aubert (CNRS\, Sorbonne Université - Université de Pa
ris)
DTSTART:20250612T150000Z
DTEND:20250612T160000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/202
DESCRIPTION:Title: NSF-CBMS conference "Representations of p-adic groups and noncomm
utative geometry"\, Lecture 8\nby Anne-Marie Aubert (CNRS\, Sorbonne U
niversité - Université de Paris) as part of Noncommutative geometry in N
YC\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/202/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anne-Marie Aubert (CNRS\, Sorbonne Université - Université de Pa
ris)
DTSTART:20250613T133000Z
DTEND:20250613T143000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/203
DESCRIPTION:Title: NSF-CBMS conference "Representations of p-adic groups and noncomm
utative geometry"\, Lecture 9\nby Anne-Marie Aubert (CNRS\, Sorbonne U
niversité - Université de Paris) as part of Noncommutative geometry in N
YC\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/203/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anne-Marie Aubert (CNRS\, Sorbonne Université - Université de Pa
ris)
DTSTART:20250613T150000Z
DTEND:20250613T160000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/204
DESCRIPTION:Title: NSF-CBMS conference "Representations of p-adic groups and noncomm
utative geometry"\, Lecture 10\nby Anne-Marie Aubert (CNRS\, Sorbonne
Université - Université de Paris) as part of Noncommutative geometry in
NYC\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/204/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jananan Arulseelan (Iowa State University)
DTSTART:20250924T190000Z
DTEND:20250924T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/205
DESCRIPTION:Title: Model Theory and an Ocneanu Ultraproduct for General Von Neumann
Algebras\nby Jananan Arulseelan (Iowa State University) as part of Non
commutative geometry in NYC\n\n\nAbstract\nThe model theories of tracial v
on Neumann algebras and\, more recently\, sigma-finite von Neumann algebra
s have led to a large body of work and applications in operator algebras.
I will discuss recent work removing the sigma-finiteness condition\, yield
ing a completely general model theory of von Neumann algebras. After revie
wing existing ultraproduct constructions in von Neumann algebras\, I will
introduce and characterize the ultraproduct corresponding to this new fram
ework and show how it generalizes important properties of the Ocneanu ultr
aproduct. I will also discuss potential future work. Partially joint work
with Goldbring\, Hart\, and Sinclair.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/205/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robert Neagu (KU Leuven)
DTSTART:20251001T190000Z
DTEND:20251001T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/206
DESCRIPTION:Title: Noncommutative coloured entropy\nby Robert Neagu (KU Leuven)
as part of Noncommutative geometry in NYC\n\n\nAbstract\nBuilding on the c
lassical noncommutative entropy for automorphisms of nuclear C*-algebras\,
I will introduce a formally different notion of entropy which uses the mo
re refined cpc approximations given by finite nuclear dimension or finite
decomposition rank. In the sequel\, I will explore the typical values of t
his entropy. This is joint work with Bhishan Jacelon.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/206/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ryo Toyota (Texas A&M)
DTSTART:20251008T190000Z
DTEND:20251008T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/207
DESCRIPTION:Title: Twisted coarse Baum-Connes conjecture and relatively hyperbolic g
roups.\nby Ryo Toyota (Texas A&M) as part of Noncommutative geometry i
n NYC\n\n\nAbstract\nCoarse Baum-Connes conjecture claims an algorithm to
compute the higher index and which has applications to important problems
in geometry\, topology and operator algebras. To verify this conjecture fo
r a larger class of metric spaces\, we introduce twisted coarse Baum–Con
nes conjecture with stable coarse algebras\, which can be viewed as a geom
etric analogue of the Baum–Connes conjecture with coefficients. We show
that this twisted version has stronger permanence properties than the clas
sical coarse Baum–Connes conjecture\, particularly with respect to union
s and subspaces. Then\, we apply this framework to relatively hyperbolic g
roups. For a finitely generated group $G$ that is hyperbolic relative to
$\\{H_1\,\\cdots\,H_n\\}$\, it is known that $G$ satisfies coarse Baum-Con
nes conjecture if each $H_i$ does and $H_i$ admits finite-dimensional simp
licial model of the universal space for proper actions. As a consequence o
f the permanence properties\, we can remove the topological condition of $
H_i$ in the aforementioned theorem. Namely\, we show that $G$ satisfies tw
isted coarse Baum-Connes conjecture with stable coefficients\, if and only
if each $H_i$ does. This is a joint work with Jintao Deng.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/207/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jeremy Hume (Carleton University)
DTSTART:20251015T190000Z
DTEND:20251015T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/208
DESCRIPTION:Title: Characterization of zero singular ideal in non-Hausdorff groupoid
C*-algebras\nby Jeremy Hume (Carleton University) as part of Noncommu
tative geometry in NYC\n\n\nAbstract\nNon-Hausdorff etale groupoids arise
naturally from interesting dynamical systems and as models of important cl
asses of $C^*$-algebras. One of the main obstacles in understanding the as
sociated $C^*$-algebras in terms of their groupoids is the existence of a
possibly non-zero ideal consisting of functions supported on meagre sets w
hich\, for instance\, obstructs characterizing simplicity in terms of the
usual groupoid properties in the Hausdorff setting. In this talk\, I discu
ss my result characterizing when this "singular" ideal is zero in terms of
a groupoid property. I will discuss the methods I use in the proofs\, inc
luding the use of the Hausdorff cover of a non-Hausdorff groupoid\, introd
uced by Timmermann\, and a new concept of "compressing" linear maps to *-h
omomorphisms. This talk is based on my preprint https://arxiv.org/abs/2509
.07262.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/208/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Enrique Pardo Espino (Universidad de Cádiz)
DTSTART:20251029T190000Z
DTEND:20251029T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/209
DESCRIPTION:Title: Categorical models for ample groupoids and their algebras\nby
Enrique Pardo Espino (Universidad de Cádiz) as part of Noncommutative ge
ometry in NYC\n\n\nAbstract\nA decade ago\, Spielberg described a new meth
od for defining $C^*$-algebras from oriented combinatorial data\, generali
zing the construction of algebras from directed graphs\, higher-rank graph
s\, and (quasi-)ordered groups. To do so\, he introduced left cancellative
small categories\, and endowed any such category with a $C^*$-algebra enc
oding categorical information\; he showed that this algebra is the groupoi
d algebra of a (sort of) Deaconu-Renault étale groupoid. \n\n"In this tal
k\, we explain the relevance of these algebras. Furthermore\, we show that
they are Exel's groupoid $C^*$-algebras associated to a suitable inverse
semigroup $\\mathcal{S}_\\Lambda$\; this would allow us characterize their
properties\, like being Hausdorff\, effective and minimal\, and thus simp
licity for these algebras. We the study groupoid actions on left cancellat
ive small categories and their associated Zappa-Szép products\, by reduci
ng them to Spielberg's model.\n\nThe contents of this talk are joint work
with Eduard Ortega (NTNU Trondheim\, Norway)."\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/209/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Forrest Glebe (University of Hawai'i\, Mānoa)
DTSTART:20251105T200000Z
DTEND:20251105T210000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/210
DESCRIPTION:Title: Characters of Bundles Associated to Almost Representations of Dis
crete Groups\nby Forrest Glebe (University of Hawai'i\, Mānoa) as par
t of Noncommutative geometry in NYC\n\n\nAbstract\nA group is said to be m
atricially stable if every function from the group to unitary matrices tha
t is "almost multiplicative" in the point-operator norm topology is "close
\," in the same topology\, to a genuine representation. A result of Dadarl
at shows that even cohomology obstructs matricial stability. The obstructi
on in his proof can be realized as follows. To each almost-representation\
, we may associate a vector bundle. This vector bundle has topological inv
ariants\, called Chern characters\, which lie in the even cohomology of th
e group. If any of these invariants are nonzero\, the almost-representatio
n is far from a genuine representation. The first Chern character can be c
omputed with the "winding number argument" of Kazhdan\, Exel\, and Loring\
, but the other invariants are harder to compute explicitly. In this talk\
, I will discuss results that allow us to compute higher invariants in spe
cific cases: when the failure to be multiplicative is scalar (joint work w
ith Marius Dadarlat) and when the failure to be multiplicative is small in
a Schatten p-norm.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/210/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Naihuan Jing (North Carolina State University)
DTSTART:20251022T190000Z
DTEND:20251022T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/211
DESCRIPTION:Title: q-Immanants and Higher Quantum Capelli Identities\nby Naihuan
Jing (North Carolina State University) as part of Noncommutative geometry
in NYC\n\n\nAbstract\nImminents are generalizations of determinants and p
ermanents. In this talk I will explain how to construct the family of pol
ynomials $S_{\\mu}(z)$ indexed by standard Young tableaux whose coefficien
ts are central elements in the quantized algebra $U_q(gl(n))$. For another
special value of $z$\, they coincide with Okounkov's quantum immanant for
the enveloping algebra gl(n). We show that the Harish-Chandra image of $
S_{\\mu}(z)$ are the factorial Schur functions. We also obtain the quantum
analogues of the higher Capelli identities and Newton-type identities\nfo
r the quantum enveloping algebra. This is joint work with Ming Liu and Ale
xander Molev.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/211/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cristian Ivanescu (MacEwan University\, Edmonton)
DTSTART:20251119T200000Z
DTEND:20251119T210000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/212
DESCRIPTION:Title: Remarks on the Cuntz Semigroup\nby Cristian Ivanescu (MacEwan
University\, Edmonton) as part of Noncommutative geometry in NYC\n\n\nAbs
tract\nThe Cuntz semigroup was introduced by J. Cuntz in the late 1970s as
a refinement of K-theory for C*-algebras. Around 2000\, A. Toms discovere
d examples of simple $C^*$-algebras that share the same Elliott invariant\
, given by K-theory\, traces\, and their pairings\, but differ in their Cu
ntz semigroups. This showed that the Cuntz semigroup captures additional s
tructure beyond the classical invariants and renewed interest in its study
.\nIn this talk\, I will give an overview of the Cuntz semigroup\, explain
its basic ideas\, and discuss some recent developments related to it. Top
ics will include the way-below relation and the notion of Cu-nuclearity.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/212/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jeff Boersema (Seattle University)
DTSTART:20260506T190000Z
DTEND:20260506T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/214
DESCRIPTION:Title: Minicourse: Real C*-algebras and K-theory\, I\nby Jeff Boerse
ma (Seattle University) as part of Noncommutative geometry in NYC\n\nAbstr
act: TBA\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/214/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jeff Boersema (Seattle University)
DTSTART:20260513T190000Z
DTEND:20260513T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/215
DESCRIPTION:Title: Minicourse: Real C*-algebras and K-theory\, II\nby Jeff Boers
ema (Seattle University) as part of Noncommutative geometry in NYC\n\nAbst
ract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/215/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jeff Boersema (Seattle University)
DTSTART:20260520T190000Z
DTEND:20260520T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/216
DESCRIPTION:Title: Minicourse: Real C*-algebras and K-theory\, III\nby Jeff Boer
sema (Seattle University) as part of Noncommutative geometry in NYC\n\nAbs
tract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/216/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arvid Siqveland (Universitetet i Sørøst-Norge)
DTSTART:20251210T200000Z
DTEND:20251210T210000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/217
DESCRIPTION:Title: Localization in Associative Rings and Associative Schemes\nby
Arvid Siqveland (Universitetet i Sørøst-Norge) as part of Noncommutativ
e geometry in NYC\n\n\nAbstract\nWe start with the argument for doing asso
ciative algebraic geometry: We need schemes of associative algebras to par
ametrize (find moduli of) noncommutative objects.\n\nLet $A$ be a commutat
ive ring. Then we can define the sheaf of rings on $X=Spec ~A$ by letting
$O_X(U)=im A\\subseteq %\\underset{m\\in U\\text{ maximal}}\n\\prod A_m\,$
and to generalize this to rings that are not necessarily commutative\, we
need a replacement for the local rings $A_m.$\nWe change our view: The in
teresting point about $A_m$ is not that it is local\, but rather that it i
s locally representing\, i.e. that in the category of pointed rings\, $mor
( m\\subset A\,-)$ is represented by $A_m.$\n\nLet $A$ be an Associative (
not necessarily commutative) ring. and let $M$ be a simple right $A$-modul
e. We prove that in the category of pointed associative rings there is a p
ointed associative ring $A_M$ representing $mor((A\,M)\,-).$ Moreover\, we
prove that for any set of $r>0$ simple modules $M=\\{M_i\\}_{i=1}^r\,$ t
he categorical product $A_M=\\prod_{i=1}^r A_{M_i}$ exists. (When $A$ is n
oncommutative\, this is certainly not the Cartesian product). Given this\,
we can define $aspec ~A$ as the set of simple right $A$-modules\, togethe
r with the contractions of such\, and we give $X=aspec ~A$ the topology ge
nerated by $\\{D(f)\\}_{f\\in A}\,$ defined in such a way that if $A$ is c
ommutative\, this is the ordinary Zariski topology. Then $O_X(U)=im A\\sub
seteq%\\underset{M\\in\\simp A\\cap U}\n\\prod A_M$ is a sheaf\, and an as
sociative scheme is a ringed space $X$ covered by affine open sets.\n\nWe
end by defining A Noncommutative Geometry. Let $Y=\\mathbb R^3\\times\\mat
hbb R^3=\\{(\\text{observer}\,\\text{observed})\\}.$ We let $\\mathbb U$ b
e the noncommutative blowup of $\\Delta\\subseteq\\mathbb R^3\\times\\math
bb R^3$ which is adding a tangent direction to each $(x\,x)\\in\\Delta.$ C
hoose a Riemannian metric on $\\mathbb R^3.$ Then the maximal velocity is
the length of the tangent vector on one side of the diagonal\, and we als
o get an opposite tangent vector on the dark side of the diagonal.\n\nEver
ything in this lecture are Turing computable\, and so everything can be co
mputed by infinitesimally deformation theory. See O.A. Laudal's book [2]
for the study of this model.\n\n\nBibliography\n\n\n\n1. E. Eriksen\, O.
A. Laudal\, A. Siqveland\,\nNoncommutative Deformation Theory. Monographs
and Research Notes in Mathematics. CRC Press\, Boka Raton\, FL\, 2017\n\n\
n\n2. O. A. Laudal\, Mathematical models in science\, World Scientific Pub
lishing Co. Pte. Ltd.\, Hackensack\, NJ\, 2021\n\n\n\n3. A. Siqveland\, \n
Associative Algebraic Geometry\,\nWorld Scientific Publishing Co. Pte. Ltd
.\, Hackensack\, NJ\, 2023\nISBN: 977-1-80061-354-6\n\n\n4. A. Siqveland\,
\nAssociative Schemes\,\\\\\nhttps://doi.org/10.48550/arXiv.2302.13843\,\n
2024\n\n\n5. A. Siqveland\,\nCountably Generated Matrix Algebras\,\\\\\nht
tps://doi.org/10.48550/arXiv.2408.01034\,\n2024\n\n\n6. A. Siqveland\,\nSh
emes of Associative Algebras\,\\\\\nhttps://doi.org/10.48550/arXiv.2410.17
703\,\n2024\n\n\n7. A. Siqveland\,\nAssociative Local Function Rings\,\\\\
\nhttps://doi.org/10.48550/arXiv.2410.16819\,\n2024\n\n\n8. A. Siqveland\,
\nCategorical Construction of Schemes\,\\\\\nhttps://arxiv.org/abs/2511.03
433\,\n2025\n\n\n9. A. Siqveland\,\nSchemes of Object in abelian Categorie
s\,\\\\\nhttp://arxiv.org/abs/2511.04191\,\n2025\n\n\n10. A. Siqveland\,\n
Localization in Associative Rings\,\\\\\nhttp://arxiv.org/abs/2511.07900\,
\n2025\n\n\n11. A. Siqveland\,\nAssociative Schemes and Subschemes\,\\\\\n
http://arxiv.org/abs/2511.09176\,\n2025\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/217/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Handelman (University of Ottawa)
DTSTART:20260128T200000Z
DTEND:20260128T210000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/218
DESCRIPTION:Title: Random walks on groups from a dimension group perspective\nby
David Handelman (University of Ottawa) as part of Noncommutative geometry
in NYC\n\n\nAbstract\nLet G be a finitely generated infinite discrete gro
up\, and let S\, containing 1\, be a finite\nsubset of G that generates it
as a semigroup (that is\, $U_{n=0}^{\\infty}S^n = G$). Let P be an elemen
t of\nthe group algebra AG (where A is either the integers or the reals)\,
whose support is S\, and\nall of whose nonzero coefficients are positive.
Then left multiplication by P is a positive\nhomomorphism $AG \\to AG$\,
and iterating it leads to an unnormalized random walk on G.\nWe can associ
ate in the obvious way the structure of a dimension group (a direct limit
of\nsimplicially ordered torsion-free abelian groups/finite-dimensional ve
ctor spaces).\n\nWe are interested in space-time cones associated to this
construction\, and the harmonic\nfunctions thereon (generalizing from the
case of abelian groups\, a method of proving even-\ntual positivity for re
peated multiplication by P)\, that reflect properties of the random\nwalk.
A natural cone arises by setting $L_n$ to be the subset of G that can be
reached by n\niterates of S starting at 1\, i.e.\, $L_n = S^n$\, and this
has the advantage that at each stage\, we\nare dealing with finite-dimensi
onal vector spaces. However\, this is still quite complicated\nand massive
ly redundant\; so we define Ln to be Sn with all points reached in fewer t
han n\nsteps deleted. This is better from the dimension group point of vie
w\, but there is now the\npossibility of dead-ends\, that is\, g in $L_n$
with $g · S\\subset S^n$ (so no gs—with s in S—belongs\nto $L_{n+
1} · S$)\, and these occur almost ubiquitously.\n\nWe first describe how
we can refine $L_n$ to avoid dead-ends without loss of information\,\nand
then study properties of the random walk that are naturally suggested by b
ehaviour\nof these new (almost-) partitions of G. Then we apply them to to
rsion-free abelian by\nfinite groups\, and show that some are much better
behaved than others\, by considering\nthe induced integral action. Then we
discuss other groups\, and in some cases\, determine\nthe pure (= extrema
l = indecomposable = ergodic) unfaithful finite harmonic functions on\nthe
m\, in particular\, for the simplest discrete Heisenberg group and the lam
plighter group.\nFinally\, we show that the quotients by the maximal order
ideals of the resulting dimension\ngroups are always ordinary stationery
dimension groups (and if A is the integers\, every\nsuch can be obtained f
or some free group and choice of P)\, so in particular\, have unique\ntrac
e. In the case of the lamplighter group\, this exhausts the unfaithful pur
e harmonic\nfunctions\, but in the case of the Heisenberg group\, don’t
even amount to a hill of traces.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/218/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arvid Siqveland (Universitetet i Sørøst-Norge)
DTSTART:20260415T190000Z
DTEND:20260415T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/219
DESCRIPTION:Title: Minicourse\, I\nby Arvid Siqveland (Universitetet i Sørøst-
Norge) as part of Noncommutative geometry in NYC\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/219/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arvid Siqveland (Universitetet i Sørøst-Norge)
DTSTART:20260422T190000Z
DTEND:20260422T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/220
DESCRIPTION:Title: Minicourse\, II\nby Arvid Siqveland (Universitetet i Sørøst
-Norge) as part of Noncommutative geometry in NYC\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/220/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arvid Siqveland (Universitetet i Sørøst-Norge)
DTSTART:20260429T190000Z
DTEND:20260429T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/221
DESCRIPTION:Title: Minicourse\, III\nby Arvid Siqveland (Universitetet i Sørøs
t-Norge) as part of Noncommutative geometry in NYC\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/221/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alessandro Vignati (Université de Paris Cité)
DTSTART:20260408T190000Z
DTEND:20260408T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/222
DESCRIPTION:Title: Rigidity of Roe-like algebras\nby Alessandro Vignati (Univers
ité de Paris Cité) as part of Noncommutative geometry in NYC\n\n\nAbstra
ct\nIn the late 80s John Roe defined a family of C*-algebras capable of de
tecting coarse geometric properties of metric spaces in operator algebraic
terms\; these are called Roe-like algebras. It is fairly elementary to sh
ow that if two metric spaces look the same in coarse geometric terms\, tha
t is\, if they are (bijectively) coarsely equivalent\, then the associated
Roe-like algebras are isomorphic. In this talk\, we investigate the conve
rse implications\, trying to extract geometric information from algebraic
data.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/222/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cédric Arhancet (University of Franche-Comté)
DTSTART:20260401T190000Z
DTEND:20260401T200000Z
DTSTAMP:20260404T111446Z
UID:NYC-NCG/223
DESCRIPTION:Title: Classical harmonic analysis viewed through the prism of noncommut
ative geometry\nby Cédric Arhancet (University of Franche-Comté) as
part of Noncommutative geometry in NYC\n\n\nAbstract\nThis talk aims to co
nnect noncommutative geometry with classical harmonic analysis on Banach s
paces\, with a particular emphasis on both classical and noncommutative $L
^p$-spaces. The overarching goal is to show how the study of operators on
$L^p$-spaces can be naturally integrated into the broader framework of non
commutative geometry\, thereby opening new perspectives in analysis.\n
LOCATION:https://stable.researchseminars.org/talk/NYC-NCG/223/
END:VEVENT
END:VCALENDAR