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BEGIN:VEVENT
SUMMARY:Mehrdad Kalantar (University of Houston\, USA)
DTSTART:20201109T150000Z
DTEND:20201109T160000Z
DTSTAMP:20260404T110914Z
UID:QGS/1
DESCRIPTION:Title: Furstenberg boundary of a discrete quantum group\nby Mehrdad Kalant
ar (University of Houston\, USA) as part of Quantum Groups Seminar [QGS]\n
\n\nAbstract\nThe notion of topological boundary actions has recently foun
d striking applications in the study of operator algebras associated to di
screte groups. We will discuss the analogue concept for discrete quantum g
roups\, show that in this generalization there still always exists a maxim
al boundary action - the so-called Furstenberg boundary. We discuss applic
ations in problems of C*-simplicity and uniqueness of the Haar state of th
e dual.\n\nThis is joint work with Pawel Kasprzak\, Adam Skalski and Rolan
d Vergnioux.\n
LOCATION:https://stable.researchseminars.org/talk/QGS/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuki Arano (Kyoto University\, Japan)
DTSTART:20201116T150000Z
DTEND:20201116T160000Z
DTSTAMP:20260404T110914Z
UID:QGS/2
DESCRIPTION:Title: On the Baum-Connes conjecture for discrete quantum groups with torsion
and the quantum Rosenberg Conjecture\nby Yuki Arano (Kyoto University\
, Japan) as part of Quantum Groups Seminar [QGS]\n\n\nAbstract\nWe give a
decomposition of the equivariant Kasparov category for a discrete quantum
group with torsions. This formulates the Baum-Connes assembly map for gene
ral discrete quantum groups possibly with torsion. As an application\, we
show that the group C*-algebra of a discrete quantum group in a certain cl
ass satisfies the UCT.\n
LOCATION:https://stable.researchseminars.org/talk/QGS/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kenny De Commer (Vrije Universiteit Brussel\, Belgium)
DTSTART:20201123T150000Z
DTEND:20201123T160000Z
DTSTAMP:20260404T110914Z
UID:QGS/3
DESCRIPTION:Title: A quantization of Sylvester's law of inertia\nby Kenny De Commer (V
rije Universiteit Brussel\, Belgium) as part of Quantum Groups Seminar [QG
S]\n\n\nAbstract\nSylvester's law of inertia states that two self-adjoint
matrices A and B are related as $A = X^*BX$ for some invertible complex ma
trix $X$ if and only if $A$ and $B$ have the same signature $(N_+\,N_-\,N_
0)$\, i.e. the same number of positive\, negative and zero eigenvalues. In
this talk\, we will discuss a quantized version of this law: we consider
the reflection equation *-algebra (REA)\, which is a quantization of the *
-algebra of polynomial functions on self-adjoint matrices\, together with
a natural adjoint action by quantum $GL(N\,\\mathbb{C})$. We then show tha
t to each irreducible bounded *-representation of the REA can be associate
d an extended signature $(N_+\,N_-\,N_0\,[r])$ with $[r]$ in $\\mathbb{R}/
\\mathbb{Z}$\, and we will explain in what way this is a complete invarian
t of the orbits under the action by quantum $GL(N\,\\mathbb{C})$. This is
part of a work in progress jointly with Stephen Moore.\n
LOCATION:https://stable.researchseminars.org/talk/QGS/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ivo Dell'Ambrogio (Université de Lille\, France)
DTSTART:20201130T150000Z
DTEND:20201130T160000Z
DTSTAMP:20260404T110914Z
UID:QGS/4
DESCRIPTION:Title: The spectrum of equivariant Kasparov theory for cyclic groups of prime
order\nby Ivo Dell'Ambrogio (Université de Lille\, France) as part of
Quantum Groups Seminar [QGS]\n\n\nAbstract\nIn 2006\, Ralf Meyer and Rysz
ard Nest proved that the G-equivariant Kasparov category of a locally comp
act group G carries the structure of a tensor-triangulated category. This
structure conveniently handles the usual homological algebra\, bootstrap c
onstructions and assembly maps involved in many KK-theoretical calculation
s\, e.g. in connection with the Baum-Connes conjecture. As with any tenso
r triangulated category\, we can also associate to the G-equivariant Kaspa
rov category its spectrum in the sense of Paul Balmer. This is a topologic
al space (similar to the Zariski spectrum of a commutative ring) which all
ows us\, as it were\, to re-inject some genuinely geometric ideas in non-c
ommutative geometry. It turns out that the spectrum contains enough inform
ation to prove the Baum-Connes conjecture for G\, hence we should expect t
he question of its computation to be very hard. In this talk\, after disc
ussing such preliminaries and motivation\, I will present joint work with
Ralf Meyer providing the state of the art on this subject. Although more g
eneral partial results are known\, a complete answer is only known so far
for finite groups of prime order and for algebras in the bootstrap categor
y.\n
LOCATION:https://stable.researchseminars.org/talk/QGS/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martijn Caspers (TU Delft\, Netherlands)
DTSTART:20201207T150000Z
DTEND:20201207T160000Z
DTSTAMP:20260404T110914Z
UID:QGS/5
DESCRIPTION:Title: Riesz transforms on compact quantum groups and strong solidity\nby
Martijn Caspers (TU Delft\, Netherlands) as part of Quantum Groups Seminar
[QGS]\n\n\nAbstract\nThe Riesz transform is one of the most important and
classical examples of a Fourier multiplier on the real numbers. It may be
described as the operator $\\nabla_j \\Delta^{-1/2}$ where $\\nabla_j = d
/dx_j$ is the derivative and $\\Delta$ is the Laplace operator. In a more
general context the Riesz transform may always be defined for any diffusio
n semigroup on the reals. In case the generator of this semi-group is the
Laplace operator the classical Riesz transform is retrieved. In quantum pr
obability the quantum Markov semi-groups play the role of the diffusion se
mi-groups and again a suitable notion of Riesz transform can be described.
\n\nWe show that the Riesz transform may be used to prove rigidity propert
ies of von Neumann algebras. We focus in particular on examples from compa
ct quantum groups. Using these tools we show that a class of quantum group
s admits rigidity properties. The class has the following properties:\n\n(
1) $\\text{SU}_q(2)$ is contained in it.\n\n(2) The class is stable under
monoidal equivalence\, free products\, dual quantum subgroups and wreath p
roducts with $S^+_N$.\n\nThe rigidity properties include the Akemann-Ostra
nd property and strong solidity. Part of this talk is based on joint work
with Mateusz Wasilewski and Yusuke Isono.\n
LOCATION:https://stable.researchseminars.org/talk/QGS/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Kyed (University of Southern Denmark\, Denmark)
DTSTART:20201214T150000Z
DTEND:20201214T160000Z
DTSTAMP:20260404T110914Z
UID:QGS/6
DESCRIPTION:Title: Dynamics of compact quantum metric spaces\nby David Kyed (Universit
y of Southern Denmark\, Denmark) as part of Quantum Groups Seminar [QGS]\n
\n\nAbstract\nThe classical Gelfand correspondence justifies the slogan th
at C*-algebras are to be thought of as "non-commutative Hausdorff spaces"
\, and Rieffel's theory of compact quantum metric spaces provides\, in th
e same vein\, a non-commutative counterpart to the theory of compact metri
c spaces. The aim of my talk is to introduce the basics of this theory\, a
nd explain some new results on dynamical systems of compact quantum metric
spaces. If time permits\, I will also touch upon another recent result\
, which shows how quantized intervals approximate a classical interval i
n the quantum version of the Gromov-Hausdorff distance. This is based on j
oint works with Jens Kaad and Thomas Gotfredsen.\n
LOCATION:https://stable.researchseminars.org/talk/QGS/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Penneys (The Ohio State University\, USA)
DTSTART:20210111T150000Z
DTEND:20210111T160000Z
DTSTAMP:20260404T110914Z
UID:QGS/7
DESCRIPTION:Title: Discrete subfactors\, realization of algebra objects\, and Q-system com
pletion\nby David Penneys (The Ohio State University\, USA) as part of
Quantum Groups Seminar [QGS]\n\n\nAbstract\nIn recent decades\, we have s
een that quantum symmetries of quantum\nmathematical objects\, like non-co
mmutative spaces and quantum field\ntheories\, are best described by quant
um groups\, subfactors\, and\nunitary tensor categories. Subfactor classif
ication has led to\ndiscovery of interesting "exotic" quantum symmetries a
nd to important\nconstructions for unitary tensor categories. For example\
, Q-systems\n(special C* Frobnius algebra objects) were introduced by Long
o to\ncharacterize the canonical endomorphism for type III subfactors\, wh
ich\nis the analog of Jones' basic construction for type $II_1$ and Kosaki
's\nversion for type III. We will use this perspective to discuss some\nsu
bfactor results which go beyond small index classification\, making\nconne
ctions to quantum groups along the way. We'll then discuss a\nversion of a
unitary higher idempotent completion for C*/W*\n2-categories based on Gai
otto-Johnson-Freyd's theory of condensations\nin higher categories.\n
LOCATION:https://stable.researchseminars.org/talk/QGS/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Julien Bichon (Université Clermont Auvergne\, France)
DTSTART:20210118T150000Z
DTEND:20210118T160000Z
DTSTAMP:20260404T110914Z
UID:QGS/8
DESCRIPTION:Title: About the monoidal invariance of cohomological dimension of Hopf algebr
as\nby Julien Bichon (Université Clermont Auvergne\, France) as part
of Quantum Groups Seminar [QGS]\n\n\nAbstract\nI will discuss the question
whether Hopf algebras having monoidally equivalent category of comodules
have the same cohomological dimension\, and I will present a new positive
answer.\n
LOCATION:https://stable.researchseminars.org/talk/QGS/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christian Voigt (University of Glasgow\, UK)
DTSTART:20210125T150000Z
DTEND:20210125T160000Z
DTSTAMP:20260404T110914Z
UID:QGS/9
DESCRIPTION:Title: Quantum Cuntz-Krieger algebras\nby Christian Voigt (University of G
lasgow\, UK) as part of Quantum Groups Seminar [QGS]\n\n\nAbstract\nThe no
tion of a quantum graph\, a concept going back to work of Erdos-Katavolos-
Shulman and Weaver\, provides a noncommutative generalisation of finite gr
aphs. Quantum graphs play an intriguing role in the analysis of quantum sy
mmetries of graphs via monoidal equivalences\, and\nnaturally appear also
in quantum information theory.\n\nIn this talk\, I will discuss the constr
uction of certain C*-algebras associated with directed quantum graphs\, in
analogy to the definition of Cuntz-Krieger algebras\, and illustrate this
with some examples. (Joint work with M. Brannan\, K. Eifler\, M. Weber.)\
n
LOCATION:https://stable.researchseminars.org/talk/QGS/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Amaury Freslon (Université Paris-Saclay\, France)
DTSTART:20210215T150000Z
DTEND:20210215T160000Z
DTSTAMP:20260404T110914Z
UID:QGS/10
DESCRIPTION:Title: How to (badly) quantum shuffle cards\nby Amaury Freslon (Universit
é Paris-Saclay\, France) as part of Quantum Groups Seminar [QGS]\n\n\nAbs
tract\nCard shuffles can be thought of as random walks on the symmetric gr
oup\, and the study of these random walks has been a subject of interest t
o probabilists for more than forty years. Even for one of the simplest exa
mples\, the random transposition walk\, precise results concerning the con
vergence to equilibrium were only very recently obtained. After briefly de
scribing that setting\, I will report on a joint work with L. Teyssier and
S. Wang where we study an analogue of the random transposition walk on th
e quantum symmetric group\, therefore a kind of "quantum card shuffle". In
particular\, we obtain a similar asymptotic description of the convergenc
e to equilibrium\, called the "limit profile"\, involving the free Poisson
distribution while the classical case involved the usual Poisson distribu
tion.\n
LOCATION:https://stable.researchseminars.org/talk/QGS/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Nakano (University of Georgia\, USA)
DTSTART:20210222T150000Z
DTEND:20210222T160000Z
DTSTAMP:20260404T110914Z
UID:QGS/11
DESCRIPTION:Title: Noncommutative Tensor Triangular Geometry\nby Daniel Nakano (Unive
rsity of Georgia\, USA) as part of Quantum Groups Seminar [QGS]\n\n\nAbstr
act\nIn this talk\, I will show how to develop a general noncommutative ve
rsion of Balmer's tensor triangular geometry that is applicable to arbitra
ry monoidal triangulated categories (M$\\Delta$C). Insights from noncommut
ative ring theory is used to obtain a framework for prime\, semiprime\, an
d completely prime (thick) ideals of an M$\\Delta$C\, $\\mathbf K $\, and
then to associate to $\\mathbf K$ a topological space --the Balmer spectru
m $\\text{Spc }{\\mathbf K}$.\n\nWe develop a general framework for (nonco
mmutative) support data\, coming in three different flavors\, and show tha
t $\\text{Spc }{\\mathbf K}$ is a universal terminal object for the first
two notions (support and weak support). The first two types of support dat
a are then used in a theorem that gives a method for the explicit classifi
cation of the thick (two-sided) ideals and the Balmer spectrum of an M$\\D
elta$C. The third type (quasi support) is used in another theorem that pro
vides a method for the explicit classification of the thick right ideals o
f $\\mathbf K$\, which in turn can be applied to classify the thick two-si
ded ideals and $\\text{Spc }{\\mathbf K}$.\n\nIf time permits applications
will be given for quantum groups and non-cocommutative finite-dimensional
Hopf algebras studied by Benson and Witherspoon.\n\nThis is joint and ong
oing work with Milen Yakimov and Kent Vashaw\n
LOCATION:https://stable.researchseminars.org/talk/QGS/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arnaud Brothier (University of New South Wales\, Australia)
DTSTART:20210308T080000Z
DTEND:20210308T090000Z
DTSTAMP:20260404T110914Z
UID:QGS/13
DESCRIPTION:Title: From subfactors to actions of the Thompson group\nby Arnaud Brothi
er (University of New South Wales\, Australia) as part of Quantum Groups S
eminar [QGS]\n\n\nAbstract\nIn his quest in constructing conformal field t
heories from subfactors Vaughan Jones found an efficient machine to constr
uct actions of groups like the Thompson groups. I will briefly explain the
story of this discovery. I will then present a general overview of those
Jones actions providing explicit examples. Some of the results presented c
ome from joint works with Vaughan Jones and with Valeriano Aiello and Robe
rto Conti.\n
LOCATION:https://stable.researchseminars.org/talk/QGS/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Réamonn Ó Buachalla (Charles University\, Czech Republic)
DTSTART:20210315T150000Z
DTEND:20210315T160000Z
DTSTAMP:20260404T110914Z
UID:QGS/14
DESCRIPTION:Title: Quantum Root Vectors and a Dolbeault Double Complex for the A-Series Q
uantum Flag Manifolds\nby Réamonn Ó Buachalla (Charles University\,
Czech Republic) as part of Quantum Groups Seminar [QGS]\n\n\nAbstract\nIn
the 2000s a series of seminal papers by Heckenberger and Kolb introduced a
n essentially unique covariant $q$-deformed de Rham complex for the irredu
cible quantum flag manifolds. In the years since\, it has become increasin
gly clear that these differential graded algebras have a central role to p
lay in the noncommutative geometry of Drinfeld-Jimbo quantum groups. Until
now\, however\, the question of how to extend Heckenberger and Kolb's con
struction beyond the irreducible case has not been examined. Here we addre
ss this question for the $A$-series Drinfeld-Jimbo quantum groups $U_q(\\f
rak{sl}_{n+1})$\, and show that for precisely two reduced decompositions o
f the longest element of the Weyl group\, Lusztig's associated space of qu
antum root vectors gives a quantum tangent space for the full quantum flag
manifold $\\mathcal{O}_q(F_{n+1})$ with associated differential graded al
gebra of classical dimension. Moreover\, its restriction to the quantum Gr
assmannians recovers the $q$-deformed complex of Heckenberger and Kolb\, g
iving a conceptual explanation for their origin. Time permitting\, we will
discuss the noncommutative Kähler geometry of thesespaces and the propos
ed extension of the root space construction to the other series. (Joint wo
rk with P. Somberg)\n
LOCATION:https://stable.researchseminars.org/talk/QGS/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrea Appel (University of Parma\, Italy)
DTSTART:20210322T150000Z
DTEND:20210322T160000Z
DTSTAMP:20260404T110914Z
UID:QGS/15
DESCRIPTION:Title: Quantum affine algebras and spectral k-matrices\nby Andrea Appel (
University of Parma\, Italy) as part of Quantum Groups Seminar [QGS]\n\n\n
Abstract\nThe Yang-Baxter equation (YBE) and the reflection equation (RE)
are two fundamental\nsymmetries in mathematics arising from particles movi
ng along a line or a half-line.\nThe quest for constant solutions of YBE (
R-matrices) is at the very origin of the Drinfeld-Jimbo\nquantum groups an
d their universal R-matrix. Similarly\, constant solutions of RE (k-matric
es)\nnaturally appear in the context of quantum symmetric pairs (QSP).\n\n
In joint work with Bart Vlaar\, we construct a discrete family of universa
l k-matrices associated to\nan arbitrary quantum symmetric Kac-Moody pair
as operators on category O integrable\nrepresentations. This generalises p
revious results by Balagovic-Kolb and Bao-Wang valid\nfor finite-type QSP.
In this talk\, I will explain how\, in affine type\, this construction gi
ves rise to\nparameter-dependent operators (spectral k-matrices) on finite
-dimensional representations of\nquantum loop algebras solving the same RE
introduced by Cherednik and Sklyanin in the 1980s\nin the context of quan
tum integrability near a boundary.\n
LOCATION:https://stable.researchseminars.org/talk/QGS/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Debashish Goswami (Indian Statistical Institute\, India)
DTSTART:20210329T140000Z
DTEND:20210329T150000Z
DTSTAMP:20260404T110914Z
UID:QGS/16
DESCRIPTION:Title: Quantum Galois Group of Subfactors\nby Debashish Goswami (Indian S
tatistical Institute\, India) as part of Quantum Groups Seminar [QGS]\n\n\
nAbstract\n(joint work with Suvrajit Bhattacharjee and Alex Chirvasitu) \n
\nIn this talk\, I prove the existence of a universal (terminal) object in
a number of categories of Hopf algebras acting on a given subfactor $N \\
subset M$ (finite index\, type $\\text{II}_1$) such that $N$ is in the fix
ed point subalgebra of the action. These universal Hopf algebras can be in
terpreted as a quantum group version of Galois group of the subfactor. We
compute such universal quantum groups for certain class of subfactors\, no
tably those coming from outer actions of finite dimensional Hopf $\\ast$ a
lgebras.\n
LOCATION:https://stable.researchseminars.org/talk/QGS/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Reutter (Max Planck Institute for Mathematics\, Germany)
DTSTART:20210412T140000Z
DTEND:20210412T150000Z
DTSTAMP:20260404T110914Z
UID:QGS/17
DESCRIPTION:Title: On fusion 2-categories\nby David Reutter (Max Planck Institute for
Mathematics\, Germany) as part of Quantum Groups Seminar [QGS]\n\n\nAbstr
act\nI will revisit and categorify concepts from the theory of fusion cate
gories — including idempotent completeness and semi-simplicity\, ultimat
ely leading to a notion of `fusion 2-category’. I will highlight structu
ral similarities and differences between fusion 1- and 2-categories and di
scuss several concrete examples. If time permits\, I will discuss the role
of fusion 2-categories as a natural building block for 4-dimensional topo
logical field theories.\n
LOCATION:https://stable.researchseminars.org/talk/QGS/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexandru Chirvasitu (University at Buffalo\, USA)
DTSTART:20210419T140000Z
DTEND:20210419T150000Z
DTSTAMP:20260404T110914Z
UID:QGS/18
DESCRIPTION:Title: Non-commutative balls and quantum group structures\nby Alexandru C
hirvasitu (University at Buffalo\, USA) as part of Quantum Groups Seminar
[QGS]\n\n\nAbstract\nThe Toeplitz algebra attached to the unit disk is the
universal C∗-algebra generated by an\nisometry\, and is a non-commutati
ve analogue of the unit disk. Similarly\, one can attach algebras to non-c
ommutative counterparts of non-compact Hermitian symmetric spaces. I will
discuss results to the effect that such quantum spaces cannot admit quantu
m group structures\, i.e. their attached non-commutative “function algeb
ras” do not admit reasonable Hopf algebra structures.\n\n(joint w/ Jacek
Krajczok and Piotr Soltan)\n
LOCATION:https://stable.researchseminars.org/talk/QGS/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Schapiro (UC Berkeley\, USA)
DTSTART:20210426T140000Z
DTEND:20210426T150000Z
DTSTAMP:20260404T110914Z
UID:QGS/19
DESCRIPTION:Title: Cluster realization of spherical DAHA\nby Alexander Schapiro (UC B
erkeley\, USA) as part of Quantum Groups Seminar [QGS]\n\n\nAbstract\nSphe
rical subalgebra of Cherednik's double affine Hecke algebra of type A admi
ts a polynomial representation in which its generators act via elementary
symmetric functions and Macdonald operators. Recognizing the elementary sy
mmetric functions as eigenfunctions of quantum Toda Hamiltonians\, and app
lying (the inverse of) the Toda spectral transform\, one obtains a new rep
resentation of spherical DAHA. In this talk\, I will discuss how this new
representation gives rise to an injective homomorphism from the spherical
DAHA into a quantum cluster algebra in such a way that the action of the m
odular group on the former is realized via cluster transformations.\n\nThe
talk is based on a joint work in progress with Philippe Di Francesco\, Ri
nat Kedem\, and Gus Schrader.\n
LOCATION:https://stable.researchseminars.org/talk/QGS/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Corey Jones (North Carolina State University\, USA)
DTSTART:20210503T140000Z
DTEND:20210503T150000Z
DTSTAMP:20260404T110914Z
UID:QGS/20
DESCRIPTION:Title: Actions of fusion categories on topological spaces\nby Corey Jones
(North Carolina State University\, USA) as part of Quantum Groups Seminar
[QGS]\n\n\nAbstract\nFusion categories are algebraic objects which genera
lize the representation categories of finite quantum groups. We define an
action of a (unitary) fusion category C on a compact Hausdorff space X to
be a C module category structure on Hilb(X)\, the category of finite dime
nsional Hilbert bundles over a compact Hausdorff space X. When X is connec
ted\, we discuss obstructions to the existence of such actions and describ
e techniques for building examples.\n
LOCATION:https://stable.researchseminars.org/talk/QGS/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rémi Boutonnet (Institut de Mathématiques de Bordeaux\, France)
DTSTART:20210510T140000Z
DTEND:20210510T150000Z
DTSTAMP:20260404T110914Z
UID:QGS/21
DESCRIPTION:Title: Non-commutative ergodic theory of semi-simple lattices\nby Rémi B
outonnet (Institut de Mathématiques de Bordeaux\, France) as part of Quan
tum Groups Seminar [QGS]\n\n\nAbstract\nIn the late 90's\, Nevo and Zimmer
wrote a series of papers describing the general structure of stationnary
actions of higher rank semi-simple Lie groups G on probability spaces. Wit
h Cyril Houdayer we extended this result in two ways: first we upgraded it
to actions on non-commutative spaces (von Neumann algebras)\, and we also
managed to study actions of lattices in G. I will explain this non-commut
ative ergodic theorem and the main ingredients of proof\, and give strikin
g consequences on the unitary representations of these lattices and their
characters.\n
LOCATION:https://stable.researchseminars.org/talk/QGS/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Laura Mančiska (University of Copenhagen\, Denmark)
DTSTART:20210524T140000Z
DTEND:20210524T150000Z
DTSTAMP:20260404T110914Z
UID:QGS/23
DESCRIPTION:Title: Quantum groups and nonlocal games\nby Laura Mančiska (University
of Copenhagen\, Denmark) as part of Quantum Groups Seminar [QGS]\n\n\nAbst
ract\nIn this talk I will explain how quantum groups arise in quantum info
rmation theory via a class of graph based nonlocal games. Our point of dep
arture will be an interactive protocol (nonlocal game) where two provers t
ry to convince a verifier that two graphs are isomorphic. Allowing provers
to take advantage of shared quantum mechanical resources will then allow
us to define quantum isomorphism of graphs as the ability of quantum playe
rs to win the corresponding game with certainty. We will see that quantum
isomorphism can be naturally reformulated in the language of quantum group
s.\n
LOCATION:https://stable.researchseminars.org/talk/QGS/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paolo Saracco (Université Libre de Bruxelles\, Belgium)
DTSTART:20210531T140000Z
DTEND:20210531T150000Z
DTSTAMP:20260404T110914Z
UID:QGS/30
DESCRIPTION:Title: Globalization for Geometric Partial Comodules\nby Paolo Saracco (U
niversité Libre de Bruxelles\, Belgium) as part of Quantum Groups Seminar
[QGS]\n\n\nAbstract\n(based on a joint work [2] with Joost Vercruysse)\n\
nThe study of partial symmetries (partial actions and coactions\, partial
representations and corepresentations\, partial comodule algebras) is a re
latively recent field in continuous expansion and\, therein\, one of the r
elevant questions is the existence and uniqueness of a so-called globaliza
tion (or enveloping action). \nFor instance\, in the framework of partial
actions of groups any global action of a group $G$ on a set induces a part
ial action of the group on any subset by restriction. The idea behind the
concept of globalization of a given partial action is to find a (universal
) $G$-set such that the initial partial action can be realized as the rest
riction of this global one.\n\nWe propose here a categorical approach to p
artial symmetries and the globalization question\, explaining several of t
he existing results and\, at the same time\, providing a procedure to cons
truct globalizations in concrete contexts of interest. Our approach relies
on the notion of geometric partial comodules\, recently introduced by Hu
and Vercruysse [1] in order to describe partial actions of algebraic group
s from a Hopf-algebraic point of view.\n\nUnlike classical partial actions
\, which exist only for (topological) groups and Hopf algebras\, geometric
partial comodules can be defined over any coalgebra in a monoidal categor
y with pullbacks and they allow to describe phenomena that are out of the
reach of the theory of partial (co)actions\, even in the Hopf algebra fram
ework. At the same time\, geometric partial comodules allow to approach in
a unified way partial actions of groups on sets\, partial coactions of Ho
pf algebras on algebras and partial (co)actions of Hopf algebras on vector
spaces.\nThus\, the question of studying the existence (and uniqueness) o
f globalization for geometric partial comodules naturally arises as a unif
ying way to address the issue.\n\nReferences:\n\n[1] J. Hu\, J.Vercruysse
- Geometrically partial actions. Trans. Amer. Math. Soc. 373 (2020)\, no.
6\, 4085-4143.\n\n[2] P. Saracco\, J. Vercruysse - Globalization for geome
tric partial comodules. Part I: general theory. Preprint (2021).\n
LOCATION:https://stable.researchseminars.org/talk/QGS/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aryan Ghobadi (Queen Mary University of London\, UK)
DTSTART:20210607T140000Z
DTEND:20210607T150000Z
DTSTAMP:20260404T110914Z
UID:QGS/31
DESCRIPTION:Title: Hopf algebras in SupLat and set-theoretical YBE solutions\nby Arya
n Ghobadi (Queen Mary University of London\, UK) as part of Quantum Groups
Seminar [QGS]\n\n\nAbstract\nSkew braces have recently attracted attentio
n as a method to study set-theoretical solutions of the Yang-Baxter equati
on. In this talk\, we will present a new approach for studying these solut
ions\, by looking at Hopf algebras in the category of complete lattices an
d join-preserving morphisms\, denoted by SupLat. Any Hopf algebra\, H in S
upLat\, has a corresponding group\, R(H)\, which we call its remnant and a
co-quasitriangular structure on H induces a brading operator on R(H)\, wh
ich induces a skew brace structure on R(H). From this correspondence\, we
will recover several aspects of the theory of skew braces. In particular\,
we will construct the universal skew brace of a set-theoretical YBE solut
ion\, as the remnant of an FRT-type reconstruction in SupLat.\n
LOCATION:https://stable.researchseminars.org/talk/QGS/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Satyajit Guin (Indian Institute of Technology Kanpur\, India)
DTSTART:20210614T140000Z
DTEND:20210614T150000Z
DTSTAMP:20260404T110914Z
UID:QGS/32
DESCRIPTION:Title: Equivariant spectral triple for the compact quantum group $U_q(2)$ for
complex deformation parameters\nby Satyajit Guin (Indian Institute of
Technology Kanpur\, India) as part of Quantum Groups Seminar [QGS]\n\n\nA
bstract\nLet $q=|q|e^{i\\pi\\theta}$ be a nonzero complex number such that
$|q|\\neq 1$\, and consider the compact quantum group $U_q(2)$. In this t
alk\, we discuss a complete list of inequivalent irreducible representatio
ns of $U_q(2)$ and its Peter-Weyl decomposition. Then\, for $\\theta\\noti
n\\mathbb{Q}\\setminus\\{0\,1\\}$\, we discuss the $K$-theory of the under
lying $C^*$-algebra $C(U_q(2))$\, and a spectral triple which is equivaria
nt under its own comultiplication action. The spectral triple obtained her
e is even\, $4^+$-summable\, non-degenerate\, and the Dirac operator acts
on two copies of the $L^2$-space of $U_q(2)$. The Chern character of the a
ssociated Fredholm module is nontrivial.\n
LOCATION:https://stable.researchseminars.org/talk/QGS/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Moritz Weber (Saarland University\, Germany)
DTSTART:20210621T140000Z
DTEND:20210621T150000Z
DTSTAMP:20260404T110914Z
UID:QGS/33
DESCRIPTION:Title: Orthogonal vs unitary in the case of "easy" quantum groups\nby Mor
itz Weber (Saarland University\, Germany) as part of Quantum Groups Semina
r [QGS]\n\n\nAbstract\nWe consider quantum subgroups of Wang’s free orth
ogonal quantum group on the one hand and of his free unitary quantum group
on the other. In the first case\, the generators of the underlying C*-alg
ebras are selfadjoint which is dropped in the latter case. We compare thes
e two cases along the lines of so called "easy" quantum groups and we obse
rve that the step from the orthogonal to the unitary case is huge. This is
a survey talk on the landscape of "easy" quantum groups with a particular
emphasis on the differences between the orthogonal and the unitary case.\
n
LOCATION:https://stable.researchseminars.org/talk/QGS/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shintaro Nishikawa (University of Münster\, Germany)
DTSTART:20210920T140000Z
DTEND:20210920T150000Z
DTSTAMP:20260404T110914Z
UID:QGS/34
DESCRIPTION:Title: Crossed products of representable localization algebras\nby Shinta
ro Nishikawa (University of Münster\, Germany) as part of Quantum Groups
Seminar [QGS]\n\n\nAbstract\nLet X be a locally compact\, Hausdorff space.
The representable localization algebra for X was introduced and studied b
y Willett and Yu. The K-theory of the algebra serves as the representable
K-homology of the space X.\n\nNow let G be a second countable\, locally co
mpact group and suppose that X is a proper G-space. It turns out that the
K-theory of the crossed product by G of the representable localization alg
ebra for X serves as the representable G-equivariant K-homology of the pro
per G-space X.\n\nThe goal of this talk is to describe these facts and rol
es of the representable localization algebras in the study of the Baum--Co
nnes conjecture.\n
LOCATION:https://stable.researchseminars.org/talk/QGS/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dominic Verdon (University of Bristol\, UK)
DTSTART:20210927T140000Z
DTEND:20210927T150000Z
DTSTAMP:20260404T110914Z
UID:QGS/35
DESCRIPTION:Title: A covariant Stinespring theorem\nby Dominic Verdon (University of
Bristol\, UK) as part of Quantum Groups Seminar [QGS]\n\n\nAbstract\nWe wi
ll introduce a finite-dimensional covariant Stinespring theorem for compac
t quantum groups. Let G be a compact quantum group\, and let T:= Rep(G) be
the rigid C*-tensor category of finite-dimensional continuous unitary rep
resentations of G. Let Mod(T) be the rigid C*-2-category of cofinite semis
imple finitely decomposable T-module categories. We show that finite-dimen
sional G-C*-algebras (a.k.a C*-dynamical systems) can be identified with e
quivalence classes of 1-morphisms out of the object T in Mod(T). For 1-mor
phisms X: T -> M1\, Y: T -> M2\, we show that covariant channels between t
he corresponding G-C*-algebras can be 'dilated' to isometries t: X -> Y \\
otimes E\, where E: M2 -> M1 is some 'environment' 1-morphism. Dilations a
re unique up to partial isometry on the environment\; in particular\, the
dilation minimising the quantum dimension of the environment is unique up
to a unitary. When G is a compact group this implies and generalises previ
ous covariant Stinespring-type theorems.\n\nWe will also discuss some resu
lts relating to rigid C*-2-categories\, including that any connected semis
imple rigid C*-2-category is equivalent to Mod(T) for some rigid C*-tensor
category T. (Here semisimple means not just semisimplicity of Hom-categor
ies but also idempotent splitting for 1-morphisms\, direct sums for object
s\, etc.)\n\nThis talk is based on the paper arXiv:2108.09872.\n
LOCATION:https://stable.researchseminars.org/talk/QGS/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Adam Skalski (IMPAN\, Poland)
DTSTART:20211004T140000Z
DTEND:20211004T150000Z
DTSTAMP:20260404T110914Z
UID:QGS/36
DESCRIPTION:Title: Gaussian states and Gaussian parts of compact quantum groups\nby A
dam Skalski (IMPAN\, Poland) as part of Quantum Groups Seminar [QGS]\n\n\n
Abstract\nI will motivate and explain the notion of a Gaussian state on a
compact quantum group G\, as introduced by Michael Schürmann. This concep
t leads to the idea of the Gaussian part of G\, understood as the smallest
quantum subgroup of G which supports all the Gaussian states of G. I will
discuss properties of Gaussian states and compute Gaussian parts for seve
ral examples. This turns out to be related to quantum connectedness and ce
rtain topological generation questions for quantum subgroups. The talk wil
l be based on joint work with Uwe Franz and Amaury Freslon.\n
LOCATION:https://stable.researchseminars.org/talk/QGS/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Julian Kranz (University of Münster\, Germany)
DTSTART:20211011T140000Z
DTEND:20211011T150000Z
DTSTAMP:20260404T110914Z
UID:QGS/37
DESCRIPTION:Title: Amenability and weak containment for étale groupoids\nby Julian K
ranz (University of Münster\, Germany) as part of Quantum Groups Seminar
[QGS]\n\n\nAbstract\nA famous theorem of Hulanicki says that a locally com
pact group is amenable if and only if its full and reduced C*-algebras coi
ncide. For groupoids\, the situation is more delicate: While amenability i
mplies equatility of the full and reduced C*-algebra\, the converse fails
according to examples by Willett. The behavior of Willett's groupoids can
be explained by their non-exactness. We show that if an étale groupoid sa
tisfies a certain exactness condition\, then equality of its full and redu
ced C*-algebra is equivalent to amenability of the groupoid.\n
LOCATION:https://stable.researchseminars.org/talk/QGS/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jonas Wahl (Hausdorff Center of Mathematics\, Germany)
DTSTART:20211025T140000Z
DTEND:20211025T150000Z
DTSTAMP:20260404T110914Z
UID:QGS/39
DESCRIPTION:Title: An introduction to diagram algebras\nby Jonas Wahl (Hausdorff Cent
er of Mathematics\, Germany) as part of Quantum Groups Seminar [QGS]\n\n\n
Abstract\nIn this talk\, I will introduce the notion of a diagram algebra
and explain their connection to the representation theory of compact quant
um groups. I will also describe the role that they play for loop models in
statistical physics as well as the correspondence between their traces an
d random walks on graphs.\n
LOCATION:https://stable.researchseminars.org/talk/QGS/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Jordan (University of Edinburgh\, UK)
DTSTART:20211101T150000Z
DTEND:20211101T160000Z
DTSTAMP:20260404T110914Z
UID:QGS/40
DESCRIPTION:Title: Cluster quantization from factorization homology\nby David Jordan
(University of Edinburgh\, UK) as part of Quantum Groups Seminar [QGS]\n\n
\nAbstract\nThe character variety of a manifold is its moduli space of fla
t G-bundles. These moduli spaces and their quantizations appear in a numbe
r of places in mathematics\, representation theory\, and quantum field the
ory. Famously\, Fock and Goncharov showed that a certain "decorated" varia
nt of character varieties carries the structure of a cluster variety -- th
at is\, the moduli space contains a distinguished set of toric charts\, wi
th combinatorially defined transitions functions (called mutations). This
led them to a now-famous quantization of their decorated character varieti
es.\n\nIn this talk I'll explain that the by-hands construction of these c
harts by Fock and Goncharov can in fact be extracted from a more general f
ramework called stratified factorization homology\, and I'll outline how t
his allows us to extend the Fock-Goncharov story from surfaces to 3-manifo
lds.\n
LOCATION:https://stable.researchseminars.org/talk/QGS/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Apurva Seth (Indian Institute of Science Education and Research -
Bhopal\, India)
DTSTART:20211108T150000Z
DTEND:20211108T160000Z
DTSTAMP:20260404T110914Z
UID:QGS/41
DESCRIPTION:Title: $C(X)$-Algebras and their K-Stability\nby Apurva Seth (Indian Inst
itute of Science Education and Research - Bhopal\, India) as part of Quant
um Groups Seminar [QGS]\n\n\nAbstract\nNon-stable K-theory is the study of
the homotopy groups of the group of (quasi-) unitaries of a $C^{*}$-algeb
ra. We will give an overview of the theory\, and discuss a special class o
f $C^{*}$-algebras\, termed as K-stable $C^{*}$-algebras along with its ra
tional analogue. We shall give a permanence property related to K-stabilit
y (rational K-stability) concerning continuous $C(X)$-algebras. We will en
d with an application of the aforementioned result to crossed product $C^{
*}$-algebras.\n
LOCATION:https://stable.researchseminars.org/talk/QGS/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Floris Elzinga (University of Oslo\, Norway)
DTSTART:20211123T100000Z
DTEND:20211123T110000Z
DTSTAMP:20260404T110914Z
UID:QGS/43
DESCRIPTION:Title: Strongly 1-Bounded Quantum Group von Neumann Algebras\nby Floris E
lzinga (University of Oslo\, Norway) as part of Quantum Groups Seminar [QG
S]\n\n\nAbstract\nStrong $1$-boundedness is a property for a tracial von N
eumann algebra $M$ that was introduced by Jung that allows one to distingu
ish $M$ from the (interpolated) free group factors. Many examples came fro
m group von Neumann algebras\, such as those from certain groups having pr
operty (T). For quantum group von Neumann algebras\, Brannan and Vergnioux
showed in a landmark paper that those coming from the orthogonal free qua
ntum groups are strongly $1$-bounded\, despite sharing many structural pro
perties with the free group factors. We first review these developments\,
and then report on recent progress concerning permanence of strong $1$-bou
ndedness under finite index subfactors and applications to quantum automor
phism groups such as the quantum permutation group $S_{N^2}^+$. This last
part is based on ongoing joint work with Brannan\, Harris\, and Yamashita.
\n\nNote the unusual day and time!\n
LOCATION:https://stable.researchseminars.org/talk/QGS/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hadewijch De Clercq (Ghent University\, Belgium)
DTSTART:20211129T150000Z
DTEND:20211129T160000Z
DTSTAMP:20260404T110914Z
UID:QGS/44
DESCRIPTION:Title: Dynamical quantum graphical calculus\nby Hadewijch De Clercq (Ghen
t University\, Belgium) as part of Quantum Groups Seminar [QGS]\n\n\nAbstr
act\nGraphical calculus provides a diagrammatic framework for performing t
opological computations with morphisms in strict tensor categories. The ke
y idea is to identify such morphisms with oriented diagrams labeled by the
ir in- and output objects. This was formalized by Reshetikhin and Turaev\,
by constructing for every strict tensor category $C$ a strict tensor func
tor that assigns isotopy classes of $C$-colored ribbon graphs to morphisms
in $C$. This can be applied to the tensor category of finite-dimensional
representations of a quantum group $U_q(g)$.\n\nIn this talk\, I will firs
t outline the fundamentals of this finite-dimensional quantum graphical ca
lculus. Then I will explain how it can be extended to a larger category of
quantum group representations\, encompassing the quantum group analog of
the BGG category $O$. In particular\, this extended framework allows to vi
sualize $U_q(g)$-intertwiners on Verma modules\, as well as morphisms depe
nding on a dynamical parameter\, such as dynamical R-matrices. Finally\, I
will describe how this dynamical quantum graphical calculus can be used t
o obtain q-difference equations for quantum spherical functions.\n\nThis t
alk is based on joint work with Nicolai Reshetikhin (UC Berkeley) and Jasp
er Stokman (University of Amsterdam)\n
LOCATION:https://stable.researchseminars.org/talk/QGS/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sophie Emma Mikkelsen (University of Southern Denmark\, Denmark)
DTSTART:20211213T150000Z
DTEND:20211213T160000Z
DTSTAMP:20260404T110914Z
UID:QGS/46
DESCRIPTION:Title: On the quantum symplectic sphere\nby Sophie Emma Mikkelsen (Univer
sity of Southern Denmark\, Denmark) as part of Quantum Groups Seminar [QGS
]\n\n\nAbstract\nThe algebra of the quantum symplectic $(4n-1)$-sphere $\\
mathcal{O}(S_q^{4n-1})$ is defined as a subalgebra of the quantum symplect
ic group by Faddeev\, Reshetikhin and Takhtajan. Recently D'Andrea and Lan
di investigated faithfull irreducible $*$-representations of $\\mathcal{O}
(S_q^{4n-1})$. They proved that the first $n-1$ generators of its envelopi
ng $C^*$-algebra $C(S_q^{4n-1})$ are all zero. The result is a generalisat
ion of the case where $n=2$ which was shown by Mikkelsen and Szymański.\n
In this talk\, I will first present how $C(S_q^{4n-1})$ can be described a
s a graph $C^*$-algebra\, from which it follows that $C(S_q^{4n-1})$ is is
omorphic to the quantum $(2n+1)$-sphere by Vaksman and Soibelman. Then\, I
present a candidate of a vector space basis for $\\mathcal{O}(S_q^{4n-1})
$ which is constructed by a nontrivial application of the Diamond lemma. T
he conjecture is supported by computer experiments for $n=1\,...\,8$. By
finding a vector space basis we can moreover conclude that the $n-1$ gener
ators are non-zero inside the algebra $\\mathcal{O}(S_q^{4n-1})$.\n
LOCATION:https://stable.researchseminars.org/talk/QGS/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jeremiah McCarthy (Munster Technological University\, Ireland)
DTSTART:20220124T150000Z
DTEND:20220124T160000Z
DTSTAMP:20260404T110914Z
UID:QGS/47
DESCRIPTION:Title: The Frucht property in the quantum group setting\nby Jeremiah McCa
rthy (Munster Technological University\, Ireland) as part of Quantum Group
s Seminar [QGS]\n\n\nAbstract\nA classical theorem of Frucht states that e
very finite group is the automorphism group of a finite graph. Is every qu
antum permutation group the quantum automorphism group of a finite graph?
In this talk we will answer this question with the help of orbits and orbi
tals. This talk is based on joint work with Teo Banica.\n
LOCATION:https://stable.researchseminars.org/talk/QGS/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Benoît Collins (Kyoto University\, Japan)
DTSTART:20220131T130000Z
DTEND:20220131T140000Z
DTSTAMP:20260404T110914Z
UID:QGS/48
DESCRIPTION:Title: A metric characterization of freeness\nby Benoît Collins (Kyoto U
niversity\, Japan) as part of Quantum Groups Seminar [QGS]\n\n\nAbstract\n
Freeness of random variables has many characterizations\, with free cumula
nts\, free entropy\, Schwinger-Dyson equations\, etc. Here\, we discuss a
new metric characterization with the norm of the sum of generators tensore
d by their adjoint\, and explain the relation and applications to other pr
oblems in operator algebras and von Neumann algebras. Time permitting\, we
will also discuss some ingredients of the proof. This is based on joint w
ork with Leonard Cadilhac.\n
LOCATION:https://stable.researchseminars.org/talk/QGS/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Simon Schmidt (University of Copenhagen\, Denmark)
DTSTART:20220207T150000Z
DTEND:20220207T160000Z
DTSTAMP:20260404T110914Z
UID:QGS/49
DESCRIPTION:Title: A graph with quantum symmetry and finite quantum automorphism group\nby Simon Schmidt (University of Copenhagen\, Denmark) as part of Quantu
m Groups Seminar [QGS]\n\n\nAbstract\nThis talk concerns quantum automorph
ism groups of graphs\, a generalization of automorphism groups of graphs i
n the framework of compact matrix quantum groups. We will focus on certain
colored graphs constructed from linear constraint systems. In particular\
, we will give an explicit connection of the solution group of the linear
constraint system and the quantum automorphism group of the corresponding
colored graph. Using this connection and a decoloring procedure\, we will
present an example of a graph with quantum symmetry and finite quantum aut
omorphism group. This talk is based on joint work with David Roberson.\n
LOCATION:https://stable.researchseminars.org/talk/QGS/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Haonan Zhang (Institute of Science and Technology Austria\, Austri
a)
DTSTART:20220214T150000Z
DTEND:20220214T160000Z
DTSTAMP:20260404T110914Z
UID:QGS/50
DESCRIPTION:Title: Lp-Lq Fourier multipliers on locally compact quantum groups\nby Ha
onan Zhang (Institute of Science and Technology Austria\, Austria) as part
of Quantum Groups Seminar [QGS]\n\n\nAbstract\nHörmander proved that the
Fourier multiplier is Lp-Lq bounded if the symbol lies in the weak Lr spa
ce\, for certain p\,q\,r. In recent years\, this result was generalized to
more general groups and quantum groups. Here we presented an extension to
certain locally compact quantum groups. It covers the known results and t
he proof is simpler. It also yields a family of Lp-Fourier multipliers ove
r compact quantum groups of Kac type. The talk is based on arXiv:2201.0834
6.\n
LOCATION:https://stable.researchseminars.org/talk/QGS/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Simeng Wang (Harbin Institute of Technology\, China)
DTSTART:20220221T140000Z
DTEND:20220221T150000Z
DTSTAMP:20260404T110914Z
UID:QGS/51
DESCRIPTION:Title: Partitions\, quantum group actions and rigidity\nby Simeng Wang (H
arbin Institute of Technology\, China) as part of Quantum Groups Seminar [
QGS]\n\n\nAbstract\nIn this talk\, I will present a new combinatorial appr
oach to the study of ergodic actions of compact quantum groups. The connec
tion between compact quantum groups and the combinatorics of partitions go
es back to Banica's founding work on the representation theory of free ort
hogonal quantum groups\, and was later formalized in the seminal paper of
Banica and Speicher under the theory of "easy quantum groups". Based on so
me new alternative version of the Tannaka-Krein reconstruction procedure f
or ergodic actions\, we extend Banica and Speicher's combinatorial approac
h to the setting of ergodic actions of compact quantum groups. Our example
s in particular recovers actions on finite spaces\, on embedded homogeneou
s spaces and on quotient spaces. Moreover\, we use this categorical point
of view to study the quantum rigidity of ergodic actions on classical spac
es\, and show that the free quantum groups cannot act ergodically on a cla
ssical connected compact space\, thereby answering a question of D. Goswam
i and H. Huang.\n\nThe talk is based on the recent preprint arXiv:2112.075
06 jointly with Amaury Freslon and Frank Taipe.\n
LOCATION:https://stable.researchseminars.org/talk/QGS/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Philipp Schmitt (Leibniz University Hannover\, Germany)
DTSTART:20220307T150000Z
DTEND:20220307T160000Z
DTSTAMP:20260404T110914Z
UID:QGS/52
DESCRIPTION:Title: Quantization of the 2-sphere\nby Philipp Schmitt (Leibniz Universi
ty Hannover\, Germany) as part of Quantum Groups Seminar [QGS]\n\n\nAbstra
ct\nThe quantization problem is the problem of associating non-commutative
quantum algebras to a classical Poisson algebra in such a way that the co
mmutator is related to the Poisson bracket. In a formal setting\, this pro
blem and its equivariant counterpart are well-understood and can always be
solved (under a mild assumption in the equivariant case). However\, in a
C*-algebraic setting\, there exist obstructions to equivariant quantizatio
n\, for example for the 2-sphere. In this talk\, we will give a brief intr
oduction to the quantization problem\, and propose a way to obtain an equi
variant quantization of the 2-sphere in a Fréchet algebraic setting.\n
LOCATION:https://stable.researchseminars.org/talk/QGS/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Suvrajit Bhattacharjee (Charles University\, Czech Republic)
DTSTART:20220328T140000Z
DTEND:20220328T150000Z
DTSTAMP:20260404T110914Z
UID:QGS/55
DESCRIPTION:Title: Braided quantum symmetries of graph C*-algebras\nby Suvrajit Bhatt
acharjee (Charles University\, Czech Republic) as part of Quantum Groups S
eminar [QGS]\n\n\nAbstract\nA braided compact quantum group (over T) is\,
roughly speaking\, a “compact quantum group” object in the category of
T-C*-algebras equipped with a twisted monoidal structure. In this talk\,
we shall explain the existence of a universal braided compact quantum grou
p acting on a graph C*-algebra in the category mentioned above. Time permi
tting\, we shall sketch the proof\, constructing along the way a braided a
nalogue of the free unitary quantum group. Finally\, as an example\, we sh
all compute this universal braided compact quantum group for the Cuntz alg
ebra.\n
LOCATION:https://stable.researchseminars.org/talk/QGS/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ali Asadi-Vasfi (Institute of Mathematics\, Czech Academy of Scien
ces\, Czech Republic)
DTSTART:20220404T140000Z
DTEND:20220404T150000Z
DTSTAMP:20260404T110914Z
UID:QGS/56
DESCRIPTION:Title: An introduction to crossed products by group actions on C*-algebras\nby Ali Asadi-Vasfi (Institute of Mathematics\, Czech Academy of Science
s\, Czech Republic) as part of Quantum Groups Seminar [QGS]\n\n\nAbstract\
nWe give a survey of some results on crossed products by discrete group ac
tions and discuss their basic properties. Further\, we restrict our attent
ion to finite group actions with the Rokhlin property\, approximate repre
sentability\, and their weakened versions. Time permitting\, we outline s
ome structure results for the crossed products by these classes of group a
ctions and their contributions to finite-dimensional quantum groups.\n
LOCATION:https://stable.researchseminars.org/talk/QGS/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pierre Bieliavsky (Université Catholique de Louvain\, Belgium)
DTSTART:20220411T140000Z
DTEND:20220411T150000Z
DTSTAMP:20260404T110914Z
UID:QGS/57
DESCRIPTION:Title: On the differential geometry of Lie groups of Fröbenius type\nby
Pierre Bieliavsky (Université Catholique de Louvain\, Belgium) as part of
Quantum Groups Seminar [QGS]\n\n\nAbstract\nThe talk will be based on the
papers.\n\n(1) In the first one\, joint with V. Gayral (Memoirs AMS 2015)
\, we construct universal deformation formulae\nfor actions on topological
algebras (C* or Fréchet) of the Lie groups which carries a negatively cu
rved left-invariant Kähler structure.\n\n(2) A second one\, joint with V.
Gayral\, S. Neshveyev and L. Tuset\, where we construct locally compact qu
antum groups from star products on a class of Lie groups.\n\nThe Lie group
s on which these deformations are performed (in both (1) and (2)) are of `
`Frobenius type''. This means that their Lie algebras carry an exact non-d
egenerate two-cocycle or\, equivalently\, that they admit an open co-adjoi
nt orbit. In both cases\, the star products\, say at the formal level\, ar
e of Fedosov type i.e. associated with a left-invariant symplectic torsion
free affine connection on the group manifold at hand. In particular\, the
y are obtained from differential theoretical considerations.\n\nHowever\,
there is a dichotomy: the orderings of the star products considered in (1)
and (2) are different. In (1)\, we deal with Weyl ordered star products\,
while in (2) with normal (or anti-normal) ones. This has\, apparently\, a
strong effect on the regularity of the categories those constructions liv
e in: smooth versus measurable or topological.\nMore precisely:\nIn (1)\,
we definitely deal with a ``smooth object''\, e.g. the universal deformati
on formula (i.e. the twist) allows to deform smooth vectors of the group a
ction\, e.g. they are relevant in differential noncommutative geometry in
the sense of A. Connes. But\, no locally compact quantum group is present
there. And until now\, I haven't be able to define a reasonable notion of
``smooth quantum group'' attached to the construction.\nIn (2)\, the quant
um group is present\, but the deformation procedure apparently breaks smoo
thness: smooth vectors of strongly continuous actions (i.e. smooth module-
algebras) of the group are not stable under twisting.\n\nIn the talk\, I w
ill discuss differential geometrical aspects of Frobenius Lie groups with
in this deformation quantization context. I will end with a suggestion bas
ed on the possible use of a Lie group theoretical version of a\nmicrolocal
analytical tool : Hörmander's smooth wave front set.\n
LOCATION:https://stable.researchseminars.org/talk/QGS/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lucas Hataishi (University of Oslo\, Norway)
DTSTART:20220516T140000Z
DTEND:20220516T150000Z
DTSTAMP:20260404T110914Z
UID:QGS/59
DESCRIPTION:Title: Yetter-Drinfeld algebras\, module categories and injectivity\nby L
ucas Hataishi (University of Oslo\, Norway) as part of Quantum Groups Semi
nar [QGS]\n\n\nAbstract\nMany examples of quantum group actions carry a Ye
tter-Drinfeld structure. Among them\, you find C*-algebras coming from the
boundary theory of Drinfeld doubles\, which is closely related to the the
ory of ucp maps and injective envelopes of Hamana. Exploring Tannaka-Krein
duality for quantum group actions\, it is possible to extend many concept
s and results of boundary theory to the categorical setting\, but the lack
of a categorification of non-braided-commutative Yetter-Drinfeld algebras
impose an obstruction to a full analogy.\n\nIn this talk\, I will sketch
how to perform such a categorification and relate it to the study of injec
tivity for module categories. Based on joint works with E. Habbestad\, S.
Neshveyev and M. Yamashita.\n
LOCATION:https://stable.researchseminars.org/talk/QGS/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sebastian Halbig (TU Dresden\, Germany)
DTSTART:20220530T140000Z
DTEND:20220530T150000Z
DTSTAMP:20260404T110914Z
UID:QGS/60
DESCRIPTION:Title: Pivotality\, twisted centres and the anti-double of a Hopf monad\n
by Sebastian Halbig (TU Dresden\, Germany) as part of Quantum Groups Semin
ar [QGS]\n\n\nAbstract\nPairs in involution are an algebraic structure who
se systematic study\nis motivated by their applications in knot theory\, r
epresentation theory and\ncyclic homology theories.\n\nIn this talk\, we w
ill explore a categorical view for these objects from the\nperspective of
representation theory of monoidal categories.\nA focus will lie on illustr
ating how their existence is linked to a particular\nwell-behaved notion o
f duality called pivotality.\nIn particular\, we will show how the languag
e of monads allows us to combine\nthe algebraic with the categorical persp
ective of these pairs.\n\nThis talk is based on the article arXiv:2201.053
61.\n
LOCATION:https://stable.researchseminars.org/talk/QGS/60/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Johan Konings (Vrije Universiteit Brussel\, Belgium)
DTSTART:20220606T140000Z
DTEND:20220606T150000Z
DTSTAMP:20260404T110914Z
UID:QGS/61
DESCRIPTION:Title: Partial algebraic quantum groups and their Drinfeld doubles\nby Jo
han Konings (Vrije Universiteit Brussel\, Belgium) as part of Quantum Grou
ps Seminar [QGS]\n\n\nAbstract\nIn this talk\, we will define partial alge
braic quantum groups\, which are special cases of weak multiplier Hopf alg
ebras\, as introduced by Van Daele and Wang. At the same time\, they provi
de a generalization to the notion of a partial compact quantum group\, as
introduced by De Commer and Timmermann. The main aim of the talk will be t
o realize the Drinfeld double of a partial compact quantum group as a part
ial algebraic quantum group. This talk is based on joint work with K. De C
ommer.\n
LOCATION:https://stable.researchseminars.org/talk/QGS/61/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Roland Vergnioux (Université de Caen\, France)
DTSTART:20220620T140000Z
DTEND:20220620T150000Z
DTSTAMP:20260404T110914Z
UID:QGS/62
DESCRIPTION:Title: Hecke algebras and the Schlichting completion for discrete quantum gro
ups\nby Roland Vergnioux (Université de Caen\, France) as part of Qua
ntum Groups Seminar [QGS]\n\n\nAbstract\nIn recent joint work with Skalski
and Voigt we construct and study the Hecke algebra and Hecke operators as
sociated with an almost normal subgroup in a discrete quantum group. We al
so give in this framework a quantum version of the Schlichting completion\
, which yields an algebraic quantum group with a compact-open subgroup. We
describe a class of examples arising from HNN extensions.\n
LOCATION:https://stable.researchseminars.org/talk/QGS/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Roberto Hernández Palomares (Texas A&M University\, USA)
DTSTART:20220627T140000Z
DTEND:20220627T150000Z
DTSTAMP:20260404T110914Z
UID:QGS/63
DESCRIPTION:Title: Q-systems and higher unitary idempotent completion for C*-algebras
\nby Roberto Hernández Palomares (Texas A&M University\, USA) as part of
Quantum Groups Seminar [QGS]\n\n\nAbstract\nQ-systems were introduced by L
ongo to study finite index inclusions of infinite von Neumann factors. A Q
-system is a unitary version of a Frobenius algebra object in a tensor cat
egory or a C* 2-category. By the work of Müger\, Q-systems give an axioma
tization of the standard invariant of a finite index subfactor.\n\nFollowi
ng work of Douglass-Reutter\, a Q-system is also a unitary version of a hi
gher idempotent. In this talk\, we will describe a higher unitary idempote
nt completion for C* 2-categories called Q-system completion.\n\nOur main
goal is to show that C*Alg\, the C* 2-category of right correspondences of
unital C*-algebras is Q-system complete. To do so\, we will use the graph
ical calculus for C* 2-categories\, and adapt a subfactor reconstruction t
echnique called realization\, which is inverse to Q-system completion. Thi
s result allows for the straightforward adaptation of subfactor results to
C*-algebras\, characterizing finite index extensions of unital C*-algebra
s equipped with a faithful conditional expectation in terms of the Q-syste
ms in C*Alg. If time allows\, we will discuss an application to induce new
symmetries of C*-algebras from old via Q-system completion.\n\nThis is jo
int work with Q. Chen\, C. Jones and D. Penneys (arXiv: 2105.12010).\n
LOCATION:https://stable.researchseminars.org/talk/QGS/63/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Harshit Yadav (Rice University\, USA)
DTSTART:20220704T140000Z
DTEND:20220704T150000Z
DTSTAMP:20260404T110914Z
UID:QGS/64
DESCRIPTION:Title: Filtered Frobenius algebras in monoidal categories\nby Harshit Yad
av (Rice University\, USA) as part of Quantum Groups Seminar [QGS]\n\n\nAb
stract\nWe develop filtered-graded techniques for algebras in monoidal\nca
tegories with the goal of establishing a categorical version of Bongale's\
n1967 result: A filtered deformation of a Frobenius algebra over a field i
s\nFrobenius as well. Towards the goal\, we construct a monoidal associate
d\ngraded functor\, building on prior works of Ardizzoni-Menini\, of Galat
ius et\nal.\, and of Gwillian-Pavlov. We then produce equivalent condition
s for an\nalgebra in a rigid monoidal category to be Frobenius in terms of
the\nexistence of categorical Frobenius form. These two results of indepe
ndent\ninterest are used to achieve our goal. As an application of our mai
n\nresult\, we show that any exact module category over a symmetric finite
\ntensor category is represented by a Frobenius algebra in it. This is joi
nt\nwork with Dr. Chelsea Walton (Rice University)\n
LOCATION:https://stable.researchseminars.org/talk/QGS/64/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Benjamin Anderson-Sackaney (Université de Caen\, France)
DTSTART:20221018T140000Z
DTEND:20221018T150000Z
DTSTAMP:20260404T110914Z
UID:QGS/65
DESCRIPTION:Title: Relative Amenability\, Amenability\, and Coamenability of Coideals
\nby Benjamin Anderson-Sackaney (Université de Caen\, France) as part of
Quantum Groups Seminar [QGS]\n\n\nAbstract\nAmenability is a deeply studie
d property of groups\, with many interesting reformulations and connection
s to the operator algebraic aspects of groups. For example\, the reduced $
C^*$-algebra $C^*_r(G)$ of a discrete group has a unique tracial state if
and only if there are no non-trivial amenable normal subgroups. This\, amo
ng other related results\, makes it apparent that the structure of the ame
nable subgroups of $G$ contains important information about $C^*_r(G)$. Fo
r a quantum group $\\mathbb{G}$\, an appropriate analogue of a subgroup is
a coideal $N\\subseteq L^\\infty(\\mathbb{G})$. We will present notions o
f relative amenability\, amenability\, and coamenability for coideals of d
iscrete and compact quantum groups motivated by "relativizations" of amena
bility and coamenability of a subgroup of a group. We will discuss the kno
wn relationships between these formally distinct notions and their relevan
ce to certain properties of the reduced $C^*$-algebras of discrete quantum
groups.\n
LOCATION:https://stable.researchseminars.org/talk/QGS/65/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Magnus Landstad (Norwegian University of Science and Technology\,
Norway)
DTSTART:20221108T150000Z
DTEND:20221108T160000Z
DTSTAMP:20260404T110914Z
UID:QGS/66
DESCRIPTION:Title: Exotic group algebras\, crossed products\, and coactions\nby Magnu
s Landstad (Norwegian University of Science and Technology\, Norway) as pa
rt of Quantum Groups Seminar [QGS]\n\n\nAbstract\nIf $G$ is a locally comp
act group\, we have the full group C*-algebra $C^*(G)$ and the reduced $C^
*_r(G)$. We call a C*-algebra properly between $C^*(G)$ and $C^*_r(G)$ exo
tic.\n\nSimilarly\, if $G$ acts on a C*-algebra $A$ we can form the full c
rossed product $C^*(G\\ltimes A)$ and the reduced crossed product $C^*_r(G
\\ltimes A)$. An exotic crossed product is a C*-algebra properly between t
he two. Work by Baum\, Guentner\, and Willett show that these algebras are
relevant to the Baum-Connes conjecture.\n\nWe think that the best way to
study these algebras is by also looking at the corresponding dual theory o
f coactions. I will discuss some of these aspects\, but there will be more
questions than answers.\n\nThis is joint work with Steve Kaliszewski and
John Quigg.\n
LOCATION:https://stable.researchseminars.org/talk/QGS/66/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alfons Van Daele (KU Leuven\, Belgium)
DTSTART:20221115T150000Z
DTEND:20221115T160000Z
DTSTAMP:20260404T110914Z
UID:QGS/67
DESCRIPTION:Title: Algebraic quantum hypergroups and duality\nby Alfons Van Daele (KU
Leuven\, Belgium) as part of Quantum Groups Seminar [QGS]\n\n\nAbstract\n
Let $G$ be a finite group and $H$ a subgroup. The set $\\mathcal{G}$ of do
uble cosets $HpH$\, with $p \\in G$ has the structure of an hypergroup. Th
e product of two elements $HpH$ and $HqH$ is the set of cosets $HrH$ where
$r \\in pHq$. The algebra $A$ of functions on $\\mathcal{G}$ is the space
of functions on $G$ that are constant on double cosets. It carries a natu
ral coproduct\, dual to the product\, and given by\n$$∆(p\,q) = \\frac{1
}{n} \\sum_{h \\in H} f(phq)$$\nwhere $n$ is the number of elements in $H$
. The dual algebra is known as the Hecke algebra associated with the pair
$G\,H$.\nIn this talk I will discuss the notion of an algebraic quantum hy
pergroup\, its fundamental properties and duality for algebraic quantum hy
pergroups.\nI will illustrate this with an example\, coming from bicrosspr
oduct theory\, constructed from a pair of closed subgroups $H$ and $K$ of
a group $G$\, with the assumption that $H \\cap K = {e}$.\nThis is part of
more general work in progress with M. Landstad (NTNU\, Trondheim)\n
LOCATION:https://stable.researchseminars.org/talk/QGS/67/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Erik Habbestad (Universityof Oslo\, Norway)
DTSTART:20221213T150000Z
DTEND:20221213T160000Z
DTSTAMP:20260404T110914Z
UID:QGS/70
DESCRIPTION:Title: C*-algebras associated to Temperley-Lieb polynomials\nby Erik Habb
estad (Universityof Oslo\, Norway) as part of Quantum Groups Seminar [QGS]
\n\n\nAbstract\nWe define Temperley-Lieb polynomials and consider the (sta
ndard) subproduct systems they generate. This subproduct system turns out
to be equivariant with respect to a compact quantum group G monoidally equ
ivalent to $U_q(2)$. Exploiting this we are able to describe the C*-algebr
as associated to the subproduct system\, which turn out to be closesly rel
ated to the linking algebra $B(U_q(2)\,G)$. This is joint work with Sergey
Neshveyev.\n
LOCATION:https://stable.researchseminars.org/talk/QGS/70/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fatemeh Khosravi (Seoul National University\, South Korea)
DTSTART:20221129T100000Z
DTEND:20221129T110000Z
DTSTAMP:20260404T110914Z
UID:QGS/72
DESCRIPTION:Title: Co-amenable quantum homogeneous spaces of compact Kac quantum groups\nby Fatemeh Khosravi (Seoul National University\, South Korea) as part
of Quantum Groups Seminar [QGS]\n\n\nAbstract\nGiven a locally compact gro
up G\, Leptin's theorem states that G is amenable if and only if the Fouri
er algebra A(G) admits a bounded approximate identity\, where the latter p
roperty is known as co-amenability of the quantum dual of G. In the quantu
m setting\, this characterization is known as the duality between amenabil
ity and co-amenability. It is proved that a discrete quantum group is amen
able if and only if its dual compact quantum group is co-amenable. The def
inition of co-amenability for quantum homogeneous spaces is given by Kalan
tar-Kasprzak-Skalski-Vergnioux. Furthermore\, they ask whether the co-amen
ability of a quantum homogeneous space is equivalent to the (relative) ame
nability of its co-dual. In this talk\, we will answer this question for q
uantum homogeneous spaces of compact Kac quantum groups under a mild assum
ption. Based on joint work with Mehrdad Kalantar.\n
LOCATION:https://stable.researchseminars.org/talk/QGS/72/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stefaan Vaes (KU Leuven\, Belgium)
DTSTART:20221122T160000Z
DTEND:20221122T170000Z
DTSTAMP:20260404T110914Z
UID:QGS/75
DESCRIPTION:Title: Quantum automorphism groups of connected locally finite graphs and qua
ntizations of finitely generated groups\nby Stefaan Vaes (KU Leuven\,
Belgium) as part of Quantum Groups Seminar [QGS]\n\n\nAbstract\nI present
a joint work with Lukas Rollier. We construct the quantum automorphism gro
up of any connected locally finite\, possibly infinite\, graph as a locall
y compact quantum group that has the classical (locally compact) automorph
ism group as a closed quantum subgroup. For finite graphs\, we get the qua
ntum automorphism group of Banica and Bichon. One of the key tools is the
construction of a unitary tensor category associated with any connected lo
cally finite graph. When this graph is the Cayley graph of a finitely gene
rated group\, the associated unitary tensor category has a canonical fiber
functor. We thus also obtain a quantization procedure for arbitrary finit
ely generated groups. In the particular example of groups defined by a tri
angle presentation\, this construction gives the property (T) discrete qua
ntum groups from earlier joint work with Valvekens.\n
LOCATION:https://stable.researchseminars.org/talk/QGS/75/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kan Kitamura (University of Tokyo\, Japan)
DTSTART:20221220T150000Z
DTEND:20221220T160000Z
DTSTAMP:20260404T110914Z
UID:QGS/77
DESCRIPTION:Title: Partial Pontryagin duality for actions of quantum groups on C*-algebra
s\nby Kan Kitamura (University of Tokyo\, Japan) as part of Quantum Gr
oups Seminar [QGS]\n\n\nAbstract\nWe compare actions on C*-algebras of two
constructions of locally compact quantum groups\, the bicrossed product d
ue to Vaes-Vainerman and the double crossed product due to Baaj-Vaes. We g
ive a one-to-one correspondence between them up to Morita equivalence\, in
the same spirit as Takesaki-Takai and Baaj-Skandalis dualities. This incl
udes a duality between a quantum double and the product of the original qu
antum group with its opposite. We will explain its consequences for equiva
riant Kasparov theory in relation to the quantum analog of the Baum-Connes
conjecture.\n
LOCATION:https://stable.researchseminars.org/talk/QGS/77/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Julia Plavnik (Indiana University Bloomington\, USA)
DTSTART:20230124T150000Z
DTEND:20230124T160000Z
DTSTAMP:20260404T110914Z
UID:QGS/78
DESCRIPTION:Title: Comparing different constructions of modular categories\nby Julia
Plavnik (Indiana University Bloomington\, USA) as part of Quantum Groups S
eminar [QGS]\n\n\nAbstract\nModular categories arise naturally in many are
as of mathematics\, such as conformal field theory\, representations of br
aid groups\, quantum groups\, and Hopf algebras\, and low dimensional topo
logy\, and they have important applications in condensed matter physics.\n
\nDespite recent progress in the classification of modular categories\, we
are still in the early stages of this theory and the general landscape re
mains largely unexplored. One important step towards deepening our underst
anding of modular categories is to have well-studied constructions. In thi
s talk\, we will present an overview of various of these constructions and
compare their properties. We will focus on ribbon zesting and symmetry ga
uging\, and we will comment on some constructions in the G-crossed setting
.\n
LOCATION:https://stable.researchseminars.org/talk/QGS/78/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthew Daws (University of Central Lancashire\, UK)
DTSTART:20230131T150000Z
DTEND:20230131T160000Z
DTSTAMP:20260404T110914Z
UID:QGS/79
DESCRIPTION:Title: Around the Approximation Property for Quantum Groups\nby Matthew D
aws (University of Central Lancashire\, UK) as part of Quantum Groups Semi
nar [QGS]\n\n\nAbstract\nI will introduce what the "approximation property
" (AP) is for (locally compact) groups\, and provide a few applications.
I will then talk about how one might give an analogous definition for (loc
ally compact) quantum groups\, explaining some of the need technology alon
g the way. Time allowing\, I will discuss how the AP interacts with vario
us common constructions\, and also about "central" versions and links with
tensor categories.\n
LOCATION:https://stable.researchseminars.org/talk/QGS/79/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oleg Aristov
DTSTART:20230207T150000Z
DTEND:20230207T160000Z
DTSTAMP:20260404T110914Z
UID:QGS/80
DESCRIPTION:Title: Complex-analytic approach to quantum groups\nby Oleg Aristov as pa
rt of Quantum Groups Seminar [QGS]\n\n\nAbstract\nWe discuss quantum analo
gues of complex Lie groups. Our approach is closer to classical quantum gr
oup theory than to C*-algebraic one (no multipliers and no invariant weigh
ts). I propose to consider a topological Hopf algebra with a finiteness co
ndition (holomorphically finitely generated or HFG for short). This topic
seems to offer a wide range of research opportunities.\n\nOur focus is on
examples\, such as analytic forms of some classical quantum groups (a def
ormation of a solvable Lie group and Drinfeld-Jimbo algebras). I also pres
ent some general results: (1) the category of Stein groups is anti-equival
ent to the category of commutative Hopf HFG algebras\; (2) If G is a compa
ctly generated Lie group\, the associated convolution cocommutative topolo
gical Hopf algebra (introduced by Akbarov) is HFG. When\, in addition\, G
is connected and linear\, the structure of this cocommutative algebra can
be described explicitly. I also plan to discuss briefly holomorphic dualit
y (which is parallel to Pontryagin duality).\n
LOCATION:https://stable.researchseminars.org/talk/QGS/80/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Devarshi Mukherjee (University of Buenos Aires\, Argentina)
DTSTART:20230221T150000Z
DTEND:20230221T160000Z
DTSTAMP:20260404T110914Z
UID:QGS/81
DESCRIPTION:Title: Noncommutative geometry in mixed characteristic\nby Devarshi Mukhe
rjee (University of Buenos Aires\, Argentina) as part of Quantum Groups Se
minar [QGS]\n\n\nAbstract\nI will give an overview of noncommutative topol
ogical algebras and their cohomology theories in the setting of the p-adic
integers.\n\nThis will entail constructions that are familiar from the co
mplex case\, such as the formation of a smooth subalgebra of a C*-algebra.
The examples I will specialise these constructions to are group algebras
of discrete and p-adic Lie groups. It turns out that these are also examp
les of bornological quantum groups (in the sense of Voigt). Finally\, if t
ime permits\, I will also discuss the computations of the Hochschild homol
ogy of the completions of such algebras.\n
LOCATION:https://stable.researchseminars.org/talk/QGS/81/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mao Hoshino (University of Tokyo\, Japan)
DTSTART:20230307T150000Z
DTEND:20230307T160000Z
DTSTAMP:20260404T110914Z
UID:QGS/82
DESCRIPTION:Title: Equivariant covering spaces of quantum homogeneous spaces\nby Mao
Hoshino (University of Tokyo\, Japan) as part of Quantum Groups Seminar [Q
GS]\n\n\nAbstract\nIn this talk I will explain the imprimitivity theorems
for equivariant correspondences in two cases: for a general compact quantu
m group under a finiteness condition\, and for the Drinfeld-Jimbo deformat
ion of a semisimple compact Lie group. These results involve the represent
ation\ntheories of function algebras and the Tannaka-Krein duality for equ
ivariant correspondences. I also would like to give some applications if t
ime allows.\n
LOCATION:https://stable.researchseminars.org/talk/QGS/82/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Melody Molander (University of California\, Santa Barbara\, USA)
DTSTART:20230314T150000Z
DTEND:20230314T160000Z
DTSTAMP:20260404T110914Z
UID:QGS/83
DESCRIPTION:Title: Skein Theory for Affine ADE Subfactor Planar Algebras\nby Melody M
olander (University of California\, Santa Barbara\, USA) as part of Quantu
m Groups Seminar [QGS]\n\n\nAbstract\nSubfactor planar algebras first were
constructed by Vaughan Jones as a diagrammatic axiomatization of the stan
dard invariant of a subfactor. These planar algebras also encode two other
invariants of the subfactors: the index and the principal graph. The Kupe
rberg Program asks to find all diagrammatic presentations of subfactor pla
nar algebras. This program has been completed for index less than 4. In th
is talk\, I will introduce subfactor planar algebras and give some present
ations of subfactor planar algebras of index 4 which have affine ADE Dynki
n diagrams as their principal graphs.\n
LOCATION:https://stable.researchseminars.org/talk/QGS/83/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arthur Troupel (Université Paris Cité\, France)
DTSTART:20230214T150000Z
DTEND:20230214T160000Z
DTSTAMP:20260404T110914Z
UID:QGS/84
DESCRIPTION:Title: Free wreath products as fundamental graph C*-algebras\nby Arthur T
roupel (Université Paris Cité\, France) as part of Quantum Groups Semina
r [QGS]\n\n\nAbstract\nThe free wreath product of a compact quantum group
by the quantum permutation group $S_N^+$ has been introduced by Bichon in
order to give a quantum counterpart of the classical wreath product. The r
epresentation theory of such groups is well-known\, but some results about
their operator algebras were still open\, for example Haagerup property\,
K-amenability or factoriality of the von Neumann algebra. I will present
a joint work with Pierre Fima in which we identify these algebras with the
fundamental C*-algebras of certain graphs of C*-algebras\, and we deduce
these properties from these constructions.\n
LOCATION:https://stable.researchseminars.org/talk/QGS/84/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yasuyuki Kawahigashi (University of Tokyo\, Japan)
DTSTART:20230328T110000Z
DTEND:20230328T120000Z
DTSTAMP:20260404T110914Z
UID:QGS/85
DESCRIPTION:Title: Topological order\, tensor networks and subfactors\nby Yasuyuki Ka
wahigashi (University of Tokyo\, Japan) as part of Quantum Groups Seminar
[QGS]\n\n\nAbstract\nI will explain interactions between two-dimensional t
opological order and subfactors from a viewpoint of tensor networks. The
range of a certain finite dimensional projection appearing in statistical
physics is identified with the higher relative commutant of the subfactor
arising from such a tensor network. We then work out the machinery of alp
ha-induction\nfor braided fusion categories in the setting of certain 4-te
nsors\, called bi-unitary connections\, appearing in subfactor theory.\n
LOCATION:https://stable.researchseminars.org/talk/QGS/85/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Brannan (University of Waterloo\, Canada)
DTSTART:20230425T140000Z
DTEND:20230425T150000Z
DTSTAMP:20260404T110914Z
UID:QGS/92
DESCRIPTION:Title: No-signalling bicorrelations and generalized quantum automorphisms of
graphs\nby Michael Brannan (University of Waterloo\, Canada) as part o
f Quantum Groups Seminar [QGS]\n\n\nAbstract\nI'll report on some recent j
oint work with Sam Harris\,\nLyudmila Turowska and Ivan Todorov (arXiv:230
2.04268)\, where we\nintroduce an analogue of bisynchronous correlations i
n the context of\nquantum input-quantum output non-local games. One of th
e main\nmotivations of this work was to find a non-local game interpretati
on of\nthe quantum automorphisms and isomorphisms of quantum graphs that h
ave\nappeared recently in the literature. I'll explain how these\nconside
rations are related to tracial representations of quantum\nautomorphism gr
oups of matrix algebras\, and in the case of ordinary\ngraphs\, lead us to
a softer (and possibly more general) notion of\nquantum symmetry for grap
hs.\n
LOCATION:https://stable.researchseminars.org/talk/QGS/92/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mainak Ghosh (Indian Statistical Institute\, India)
DTSTART:20230620T090000Z
DTEND:20230620T100000Z
DTSTAMP:20260404T110914Z
UID:QGS/98
DESCRIPTION:Title: Unitary connections and Q-systems\nby Mainak Ghosh (Indian Statist
ical Institute\, India) as part of Quantum Groups Seminar [QGS]\n\n\nAbstr
act\nThe standard invariant plays a major role in subfactor theory. In thi
s talk\, I will discuss a 2-categorical generalization of an axiomatizatio
n of the standard invariant and further discuss some algebraic structures
associated to it. This is based on joint work with P. Das\, S. Ghosh and C
. Jones (arXiv:2211.03822) and on arxiv : 2302.04921.\n
LOCATION:https://stable.researchseminars.org/talk/QGS/98/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joeri De Ro (Vrije Universiteit Brussel\, Belgium)
DTSTART:20230606T140000Z
DTEND:20230606T150000Z
DTSTAMP:20260404T110914Z
UID:QGS/100
DESCRIPTION:Title: Actions of compact and discrete quantum groups on operator systems\nby Joeri De Ro (Vrije Universiteit Brussel\, Belgium) as part of Quantu
m Groups Seminar [QGS]\n\n\nAbstract\nWe introduce the notion of an action
of a discrete or compact quantum group on an operator system\, and study
equivariant operator system injectivity. Given an action of a discrete qua
ntum group on an operator system X\, we introduce associated crossed produ
cts\, and we prove that equivariant injectivity of the operator system X i
s equivalent with dual equivariant injectivity of the associated crossed p
roducts. As an application of this result\, we prove a duality result for
equivariant injective envelopes. This is joint work with Lucas Hataishi.\n
LOCATION:https://stable.researchseminars.org/talk/QGS/100/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mateusz Wasilewski (IMPAM\, Poland)
DTSTART:20231016T140000Z
DTEND:20231016T150000Z
DTSTAMP:20260404T110914Z
UID:QGS/101
DESCRIPTION:Title: Quantum Cayley graphs\nby Mateusz Wasilewski (IMPAM\, Poland) as
part of Quantum Groups Seminar [QGS]\n\n\nAbstract\nI will talk about a me
thod of associating a quantum graph to a discrete quantum group together w
ith a projection in its function algebra. These quantum graphs are analogu
es of Cayley graphs and they do not depend on the choice of a generating p
rojection in the sense of metric geometry. Later I will show how they can
help in finding examples of finite quantum groups having Frucht property\,
i.e. arising as quantum automorphism groups of quantum graphs.\n\nPart of
the talk will be based on an on-going joint work with Michael Brannan and
Adam Skalski.\n
LOCATION:https://stable.researchseminars.org/talk/QGS/101/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Amaury Freslon (Université Paris-Saclay\, France)
DTSTART:20231023T140000Z
DTEND:20231023T150000Z
DTSTAMP:20260404T110914Z
UID:QGS/102
DESCRIPTION:Title: Classical actions of quantum permutations\nby Amaury Freslon (Uni
versité Paris-Saclay\, France) as part of Quantum Groups Seminar [QGS]\n\
n\nAbstract\nQuantum permutation groups can act non-trivially\, and even e
rgodically\, on finite spaces. This is\, in view of many quantum rigidity
results\, an exception and it is natural to wonder whether there are other
classical spaces on which quantum permutations can act. H. Huang construc
ted a family of such spaces\, and we will show that these are the only pos
sibilities. This is a joint work with F. Taipe and S. Wang.\n
LOCATION:https://stable.researchseminars.org/talk/QGS/102/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Siegfried Echterhoff (WWU Münster\, Germany)
DTSTART:20231204T150000Z
DTEND:20231204T160000Z
DTSTAMP:20260404T110914Z
UID:QGS/103
DESCRIPTION:Title: Proper actions\, fixed-point algebras\, and deformation via coactions
\nby Siegfried Echterhoff (WWU Münster\, Germany) as part of Quantum
Groups Seminar [QGS]\n\n\nAbstract\nThe notion of proper actions of groups
on spaces has various generalizations for group actions of noncommutative
$C^*$-algebras $A$\, which all allow the construction of generalized fixe
d-point algebras $A^G$ which are Morita equivalent to ideals in the reduce
d crossed products $A\\rtimes_rG$. The weakest version was introduced by
Rieffel in 1990 and it played an important role in his theory of deformat
ions via actions of $\\mathbb R^d$. In this talk we want to report on some
joint work with Alcides Buss on a version of proper actions which allows
the construction of maximal (or exotic) generalized fixed-point algebras w
hich are Morita equivalent to ideals in the maximal (resp. exotic) crossed
products. We will report on several applications including Landstad duali
ty for coactions and deformation of C*-algebras via coactions in the sense
of Kasprzak and Bowmick\, Neshveyev\, and Sangha.\n
LOCATION:https://stable.researchseminars.org/talk/QGS/103/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Benjamin Anderson-Sackaney (Université de Caen\, France)
DTSTART:20231113T150000Z
DTEND:20231113T160000Z
DTSTAMP:20260404T110914Z
UID:QGS/104
DESCRIPTION:Title: Topological Boundaries of Representations and Coideals\nby Benjam
in Anderson-Sackaney (Université de Caen\, France) as part of Quantum Gro
ups Seminar [QGS]\n\n\nAbstract\nWe will introduce and study quantum analo
gues of Furstenberg-Hamana boundaries of representations of discrete quant
um groups\, where the Furstenberg boundary is the Furstenberg-Hamana bound
ary of the left regular representation. Our focus is on the GNS representa
tions of idempotent states\, or to put it differently\, the quasi-regular
representations coming from coideals associated to compact quasi-subgroups
. We use their Furstenberg-Hamana boundaries to study (co)amenability prop
erties of such coideals. Then\, we combine our work with recent work of Ha
taishi and De Ro to settle open problems of Kalantar\, Kasprzak\, Skalski\
, and Vergnioux for wide classes of quantum groups\, including unimodular
discrete quantum groups and C*-exact discrete quantum groups. For example\
, we prove that a unimodular discrete quantum group has the unique trace p
roperty iff it acts faithfully on its Furstenberg boundary.\n\nThis is joi
nt work with Fatemeh Khosravi.\n
LOCATION:https://stable.researchseminars.org/talk/QGS/104/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robert Yuncken (Université de Lorraine\, France)
DTSTART:20231120T150000Z
DTEND:20231120T160000Z
DTSTAMP:20260404T110914Z
UID:QGS/105
DESCRIPTION:Title: Crystallizing compact semisimple Lie groups\nby Robert Yuncken (U
niversité de Lorraine\, France) as part of Quantum Groups Seminar [QGS]\n
\n\nAbstract\nThe theory of crystal bases is a means of simplifying the re
presentation theory of semisimple Lie algebras by passing through quantum
groups. Varying the parameter q of the quantized enveloping algebras\, we
pass from the classical theory at $q=1$ through the Drinfeld-Jimbo alg
ebras at $q\\in]0\,1[$ to the crystal limit at $q = 0$. At this point\, th
e main features of the representation theory crystallize into purely combi
natorial data described by crystal graphs. In this talk\, we will describ
e what happens to the C*-algebra of functions on a compact semisimple Lie
group under the crystallization process\, yielding higher-rank graph algeb
ras. This is joint work with Marco Matassa.\n
LOCATION:https://stable.researchseminars.org/talk/QGS/105/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Malte Gerhold (Saarland University\, Germany)
DTSTART:20231127T150000Z
DTEND:20231127T160000Z
DTSTAMP:20260404T110914Z
UID:QGS/106
DESCRIPTION:Title: Cohomology of free unitary quantum groups\nby Malte Gerhold (Saar
land University\, Germany) as part of Quantum Groups Seminar [QGS]\n\n\nAb
stract\nIn the talk\, we will discuss the free unitary quantum groups\n(or
"universal quantum groups") of Wang and van Daele from a\n(co)homological
perspective. We find a free resolution of the\ncounit\, a versatile tool
which helps to compute cohomological data such\nas Hochschild cohomology o
r bialgebra cohomology of the associated Hopf\nalgebras. For free orthogon
al quantum groups\, such resolutions have been\nfound by Collins\, Härtel
\, and Thom (in the Kac-case) and Bichon (in the\ngeneral case)\, and they
will serve as our starting point for finding\nresolutions for free unitar
y quantum groups.\n\nBased on joint work with I. Baraquin\, U. Franz\, A.
Kula and M. Tobolski\n[arXiv:2309.07767]
\n
LOCATION:https://stable.researchseminars.org/talk/QGS/106/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Uwe Franz (Université de Franche-Comté\, France)
DTSTART:20240122T150000Z
DTEND:20240122T160000Z
DTSTAMP:20260404T110914Z
UID:QGS/107
DESCRIPTION:Title: Gaussian Parts of Compact Quantum Groups\nby Uwe Franz (Universit
é de Franche-Comté\, France) as part of Quantum Groups Seminar [QGS]\n\n
\nAbstract\nWe introduce the Gaussian part of a compact quantum group G\,
namely the largest quantum subgroup of G supporting all the Gaussian funct
ionals of G. We prove that the Gaussian part is always contained in the Ka
c part\, and characterise Gaussian parts of classical compact groups\, dua
ls of classical discrete groups and q-deformations of compact Lie groups.
The notion turns out to be related to a new concept of "strong connectedne
ss" and we exhibit several examples of both strongly connected and totally
strongly disconnected compact quantum groups. Joint work with Amaury Fres
lon and Adam Skalski.\n
LOCATION:https://stable.researchseminars.org/talk/QGS/107/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joeri De Ro (Vrije Universiteit Brussel\, Belgium)
DTSTART:20240129T150000Z
DTEND:20240129T160000Z
DTSTAMP:20260404T110914Z
UID:QGS/108
DESCRIPTION:Title: Equivariant injectivity of crossed products\nby Joeri De Ro (Vrij
e Universiteit Brussel\, Belgium) as part of Quantum Groups Seminar [QGS]\
n\n\nAbstract\nWe introduce the notion of a G-operator space\, which consi
sts of an action of a locally compact quantum group G on an operator space
X\, and we study the notion of G-equivariant injectivity for such an oper
ator space. We define a natural associated crossed product operator space
X ⋊ G\, on which both the locally compact quantum group G and its dual a
ct. We completely characterise when these crossed products are equivariant
ly injective with respect to these actions. We discuss how these results g
eneralise and unify several recent results from the literature and we give
some new applications.\n
LOCATION:https://stable.researchseminars.org/talk/QGS/108/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergio Girón Pacheco (KU Leuven\, Belgium)
DTSTART:20240205T150000Z
DTEND:20240205T160000Z
DTSTAMP:20260404T110914Z
UID:QGS/109
DESCRIPTION:Title: Intertwining techniques for actions of C*-tensor categories\nby S
ergio Girón Pacheco (KU Leuven\, Belgium) as part of Quantum Groups Semin
ar [QGS]\n\n\nAbstract\nIntertwining techniques\, first used in the realm
of C*-algebras in Elliott’s classification of AF-algebras\, have been es
sential in the classification theory of C*-algebras and their group action
s. In this talk I will discuss intertwining and how it appears in C*-class
ification\, I will then outline an adaptation of these techniques to the t
ensor category equivariant setting. Time permitting I will discuss an appl
ication of these techniques to the study of tensor category equivariant Ji
ang-Su stability.\n
LOCATION:https://stable.researchseminars.org/talk/QGS/109/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kent Vashaw (Massachusetts Institute of Technology\, USA)
DTSTART:20240212T150000Z
DTEND:20240212T160000Z
DTSTAMP:20260404T110914Z
UID:QGS/110
DESCRIPTION:Title: Quantum-symmetric equivalence via Manin's universal quantum groups\nby Kent Vashaw (Massachusetts Institute of Technology\, USA) as part of
Quantum Groups Seminar [QGS]\n\n\nAbstract\nWe study 2-cocycle (and more
generally quantum-symmetric equivalences between) twists of graded algebra
s via their associated universal quantum groups\, in the sense of Manin. W
e prove that Zhang twists arise as a special case of 2-cocycle twist\, and
that 2-cocyle twisting preserves many fundamental homological invariants
of graded algebras. As a consequence\, we give a characterization of Artin
--Schelter regular algebras using the language of 2-cocycle twists.\n
LOCATION:https://stable.researchseminars.org/talk/QGS/110/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lyudmila Turowska (Chalmers University of Technology and Universit
y of Gothenburg\, Sweden)
DTSTART:20240304T150000Z
DTEND:20240304T160000Z
DTSTAMP:20260404T110914Z
UID:QGS/111
DESCRIPTION:Title: No-signalling values of cooperative quantum games\nby Lyudmila Tu
rowska (Chalmers University of Technology and University of Gothenburg\, S
weden) as part of Quantum Groups Seminar [QGS]\n\n\nAbstract\nFinding valu
es\, the optimal winning probability\, of various non-local games over dif
ferent strategies has been an important task in Quantum Information Theory
and also for resolving the Connes Embedding Problem. In this talk I will
discuss values of quantum games (games with quantum inputs and outputs)\,
arising from the type hierarchy of quantum no-signalling correlations\, es
tablishing operator space tensor norm expressions for each of the correlat
ion types. This is a joint work with Jason Crann\, Rupert Levene and Ivan
Todorov.\n
LOCATION:https://stable.researchseminars.org/talk/QGS/111/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robert Laugwitz (University of Nottingham\, UK)
DTSTART:20240219T150000Z
DTEND:20240219T160000Z
DTSTAMP:20260404T110914Z
UID:QGS/112
DESCRIPTION:Title: Induced functors on Drinfeld centers\nby Robert Laugwitz (Univers
ity of Nottingham\, UK) as part of Quantum Groups Seminar [QGS]\n\n\nAbstr
act\nI will explain how the right/left adjoint of a monoidal functor induc
ed a braided lax/oplax monoidal functors between the corresponding Drinfel
d centers. This requires some mild technical assumptions\, namely that the
projection formulas hold for the adjoint functor. This holds\, for exampl
e\, when the monoidal categories are rigid. As the induced functors on the
Drinfeld centers are (op)lax and compatible with braiding\, they preserve
commutative (co)algebra objects. As classes of examples\, we consider mon
oidal restriction functors along extensions of Hopf algebras leading to (c
o)induction functors on Yetter-Drinfeld module categories. This is joint w
ork in progress with Johannes Flake (Bonn) and Sebastian Posur (Münster).
\n
LOCATION:https://stable.researchseminars.org/talk/QGS/112/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Victor Ostrik (University of Oregon\, USA)
DTSTART:20240311T170000Z
DTEND:20240311T180000Z
DTSTAMP:20260404T110914Z
UID:QGS/113
DESCRIPTION:Title: Growth in tensor powers\nby Victor Ostrik (University of Oregon\,
USA) as part of Quantum Groups Seminar [QGS]\n\n\nAbstract\nThis talk is
based on joint work with K. Coulembier\, P. Etingof\, D. Tubbenhauer. Let
$G$ be any group and let $V$ be a finite dimensional representation of $G$
over some field. We consider tensor powers of $V$ and their decomposition
s into indecomposable summands. The main question which will be addressed
in this talk: what can we say about count (e.g. total number) of these ind
ecomposable summands? It turns out that there are reasonable partial answe
rs to this question asymptotically\, i.e. when the tensor power is large.\
n\nPlease note the unusual time\n
LOCATION:https://stable.researchseminars.org/talk/QGS/113/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chiara Esposito (University of Salerno\, Italy)
DTSTART:20240513T140000Z
DTEND:20240513T150000Z
DTSTAMP:20260404T110914Z
UID:QGS/114
DESCRIPTION:Title: Equivariant formality and reduction\nby Chiara Esposito (Universi
ty of Salerno\, Italy) as part of Quantum Groups Seminar [QGS]\n\n\nAbstra
ct\nIn this talk\, we discuss the reduction-quantization diagram in terms
of formality. First\, we propose a reduction scheme for multivector fields
and multidifferential operators\, phrased in terms of L-infinity morphism
s. This requires the introduction of equivariant multivector fields and eq
uivariant multidifferential operator complexes\, which encode the informat
ion of the Hamiltonian action\, i.e.\, a G-invariant Poisson structure all
owing for a momentum map. As a second step\, we discuss an equivariant ver
sion of the formality theorem\, conjectured by Tsygan and recently solved
in a joint work with Nest\, Schnitzer\, and Tsygan. This result has immedi
ate consequences in deformation quantization\, since it allows for obtaini
ng a quantum moment map from a classical momentum map with respect to a G-
invariant Poisson structure.\n
LOCATION:https://stable.researchseminars.org/talk/QGS/114/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Edward Pearce-Crump (Imperial College London\, UK)
DTSTART:20240520T140000Z
DTEND:20240520T150000Z
DTSTAMP:20260404T110914Z
UID:QGS/115
DESCRIPTION:Title: Compact Matrix Quantum Group Equivariant Neural Networks\nby Edwa
rd Pearce-Crump (Imperial College London\, UK) as part of Quantum Groups S
eminar [QGS]\n\n\nAbstract\nIn deep learning\, we would like to develop pr
incipled approaches for constructing neural networks. One important approa
ch involves identifying symmetries that are inherent in data and then enco
ding them into neural network architectures using representations of group
s. However\, there exist so-called “quantum symmetries” that cannot be
understood formally by groups. In this talk\, we show how to construct ne
ural networks that are equivariant to compact matrix quantum groups using
Woronowicz’s version of Tannaka-Krein duality. We go on to characterise
the linear weight matrices that appear in these neural networks for a clas
s of compact matrix quantum groups known as “easy”. In particular\, w
e show that every compact matrix group equivariant neural network is a com
pact matrix quantum group equivariant neural network.\n
LOCATION:https://stable.researchseminars.org/talk/QGS/115/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jacek Krajczok (Vrije Universiteit Brussel\, Belgium)
DTSTART:20240527T140000Z
DTEND:20240527T150000Z
DTSTAMP:20260404T110914Z
UID:QGS/116
DESCRIPTION:Title: Modular invariants of quantum groups\nby Jacek Krajczok (Vrije Un
iversiteit Brussel\, Belgium) as part of Quantum Groups Seminar [QGS]\n\n\
nAbstract\nA very interesting feature of compact quantum groups is that th
eir Haar integral\, which is a normal state on $L^{\\infty}(G)$\, can be n
on-tracial. Via Tomita-Takesaki theory\, this gives rise to two groups of
automorphisms: modular automorphisms and scaling automorphisms. One can us
e them to define a number of invariants\, related to whether these automor
phisms are trivial\, inner or approximately inner. During the talk I'll in
troduce such invariants (also in the general locally compact case)\, discu
ss a conjecture related to one of them\, and present their calculation in
the case of q-deformed compact\, simply connected\, semisimple Lie group $
G_q$. The talk is based on a joint work with Piotr Sołtan.\n
LOCATION:https://stable.researchseminars.org/talk/QGS/116/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ken Goodearl (Universite of California Santa Barbara\, USA)
DTSTART:20240624T070000Z
DTEND:20240624T080000Z
DTSTAMP:20260404T110914Z
UID:QGS/117
DESCRIPTION:Title: Spectra of quantum algebras\nby Ken Goodearl (Universite of Calif
ornia Santa Barbara\, USA) as part of Quantum Groups Seminar [QGS]\n\n\nAb
stract\nThe talk will survey what is known and/or conjectured about the pr
ime and primitive spectra of quantum algebras\, particularly quantized coo
rdinate rings and related algebras such as quantized Weyl algebras. The to
pological structure of these spectra\, their relations with classical alge
braic varieties\, and their relations with each other will be discussed.\n
LOCATION:https://stable.researchseminars.org/talk/QGS/117/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Roland Vergnioux (Université de Caen\, France)
DTSTART:20240603T140000Z
DTEND:20240603T150000Z
DTSTAMP:20260404T110914Z
UID:QGS/118
DESCRIPTION:Title: Maximal amenability of the radial subalgebra in free quantum groups f
actors\nby Roland Vergnioux (Université de Caen\, France) as part of
Quantum Groups Seminar [QGS]\n\n\nAbstract\nThe free orthogonal quantum gr
oups $O^+(N)$\, introduced by Shuzhou Wang\, are monoidally equivalent to
the $SU_q(2)$ compact quantum groups\, but on an analytical level they beh
ave much like the quantum duals of the classical free groups\, when $N > 2
$. I will review their definition and main properties\, and present a new
result about the maximal amenability of the associated radial MASA\, obtai
ned in recent joint work with Xumin Wang.\n
LOCATION:https://stable.researchseminars.org/talk/QGS/118/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Gromada (Czech Technical University\, Czechia)
DTSTART:20240617T140000Z
DTEND:20240617T150000Z
DTSTAMP:20260404T110914Z
UID:QGS/119
DESCRIPTION:Title: Cayley graphs: Symmetries\, quantizations\, and duality\nby Danie
l Gromada (Czech Technical University\, Czechia) as part of Quantum Groups
Seminar [QGS]\n\n\nAbstract\nIn the talk\, we are going to quantize sever
al aspects of Cayley graphs. First\, we are going to study quantum symmetr
ies of Cayley graphs of abelian groups. From the classical theory\, it is
known that the Fourier transform diagonalizes the adjacency matrix of any
such Cayley graph.\nThis can be used to determine the graph's quantum auto
morphism group. Secondly\, we are going to show\, how to quantize Cayley g
raphs of abelian groups. We obtain a quantum graph by twisting the functio
n algebra of the classical one. Finally\, we recall a classical\nconstruct
ion that takes a distance regular Cayley graph of an abelian group or\, mo
re generally\, a translation association scheme and constructs its dual by
applying the Fourier transform. We generalize this construction replacing
abelian groups by arbitrary finite quantum groups.\n
LOCATION:https://stable.researchseminars.org/talk/QGS/119/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marco Matassa (Oslo Metropolitan University\, Norway)
DTSTART:20240701T140000Z
DTEND:20240701T150000Z
DTSTAMP:20260404T110914Z
UID:QGS/120
DESCRIPTION:Title: Equivariant quantizations of the positive nilradical and covariant di
fferential calculi\nby Marco Matassa (Oslo Metropolitan University\, N
orway) as part of Quantum Groups Seminar [QGS]\n\n\nAbstract\nWe consider
the problem of quantizing the positive nilradical of a complex semisimple
Lie algebra of finite rank\, together with a certain fixed direct sum deco
mposition. The decompositions we consider are in one-to-one correspondence
with total orders on the simple roots\, and exhibit the nilradical as a d
irect sum of graded modules for appropriate Levi factors. We show that thi
s situation can be quantized equivariantly as a finite-dimensional subspac
e within the positive part of the corresponding quantized enveloping algeb
ra. Furthermore\, we show that such subspaces give rise to left coideals\,
with the possible exception of components corresponding to some exception
al Lie algebras\, and this property singles them out uniquely. Finally\, w
e discuss how to use these quantizations to construct covariant first-orde
r differential calculi on quantum flag manifolds\, which coincide with tho
se introduced by Heckenberger-Kolb in the irreducible case.\n
LOCATION:https://stable.researchseminars.org/talk/QGS/120/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lukas Rollier (Katholieke Universiteit Leuven\, Belgium)
DTSTART:20240610T140000Z
DTEND:20240610T150000Z
DTSTAMP:20260404T110914Z
UID:QGS/121
DESCRIPTION:Title: Quantum automorphism groups of discrete structures\nby Lukas Roll
ier (Katholieke Universiteit Leuven\, Belgium) as part of Quantum Groups S
eminar [QGS]\n\n\nAbstract\nGiven any mathematical structure\, it is a nat
ural question to ask which quantum symmetries it admits. One can in genera
l not hope to find a quantum automorphism group for any structure in the f
ramework of Kustermans-Vaes\, as a necessary condition for its existence i
s local compactness of the classical automorphism group. In recent work\,
a wide range of discrete structures\, those which are connected and locall
y finite in a suitable sense\, were shown to admit an algebraic quantum au
tomorphism group. The main tool for their construction is a generalization
of the Tannaka-Krein-Woronowicz reconstruction theorem. In particular\, t
his allows to construct quantum automorphism groups of connected locally f
inite quantum graphs\, such as Wasilewski's quantum Cayley graphs\, genera
lizing joint results with Stefaan Vaes.\n
LOCATION:https://stable.researchseminars.org/talk/QGS/121/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jean Delhaye (Université Paris-Saclay\, France)
DTSTART:20241118T150000Z
DTEND:20241118T160000Z
DTSTAMP:20260404T110914Z
UID:QGS/122
DESCRIPTION:Title: Cutoff for the Brownian Motion on the Unitary Quantum Group\nby J
ean Delhaye (Université Paris-Saclay\, France) as part of Quantum Groups
Seminar [QGS]\n\n\nAbstract\nWe introduce an analog of the Brownian motion
on free unitary quantum groups UN+. We will discuss the construction o
f this Brownian motion\, computing its cutoff\, where convergence to equil
ibrium undergoes a sharp transition. We will also examine the cutoff profi
le\, analyzing the fine-scale behavior of the total variation distance aro
und the cutoff. Unlike classical or orthogonal quantum groups\, the study
of UN+ has additional challenges\, such as non-absolute continuity\, di
stinct properties of its central algebra and inabilities to clearly identi
fy a Brownian motion.\n
LOCATION:https://stable.researchseminars.org/talk/QGS/122/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Malte Leimbach (Radboud University\, Netherlands)
DTSTART:20241216T150000Z
DTEND:20241216T160000Z
DTSTAMP:20260404T110914Z
UID:QGS/123
DESCRIPTION:Title: Convergence of Peter-Weyl Truncations of Compact Quantum Groups\n
by Malte Leimbach (Radboud University\, Netherlands) as part of Quantum Gr
oups Seminar [QGS]\n\n\nAbstract\nA fundamental principle of noncommutativ
e geometry is to encode geometric information by spectral data\, formalis
ed in the notion of spectral triples. In physical practice there are\, ho
wever\, always obstructions on the availability of such data\, and one mi
ght be led to considering truncated versions of spectral triples instead.
In this talk we will take a closer look at this formalism and explore it
within the framework of compact quantum metric spaces. In particular we w
ill consider compact quantum groups as compact quantum metric spaces when
equipped with an invariant lip-norm. We will discuss complete Gromov-Haus
dorff convergence of truncations arising from the Peter-Weyl decompositio
n of a compact quantum group.\n
LOCATION:https://stable.researchseminars.org/talk/QGS/123/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Julio Cáceres (Vanderbilt University\, USA)
DTSTART:20250203T150000Z
DTEND:20250203T160000Z
DTSTAMP:20260404T110914Z
UID:QGS/125
DESCRIPTION:Title: New hyperfinite subfactors with infinite depth\nby Julio Cáceres
(Vanderbilt University\, USA) as part of Quantum Groups Seminar [QGS]\n\n
\nAbstract\nWe will present new examples of irreducible\, hyperfinite subf
actors with trivial standard invariant and interesting Jones indices. Thes
e are obtained by constructing new finite dimensional commuting squares. W
e will use two graph planar algebra embedding theorems and the classificat
ion of small index subfactors to show that our commuting square subfactors
cannot have finite depth. We also present one-parameter families of commu
ting squares that\, by a classification result of Kawahigashi\, will also
yield irreducible infinite depth subfactors. This is joint work with Dietm
ar Bisch.\n
LOCATION:https://stable.researchseminars.org/talk/QGS/125/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hua Wang (Harbin Institute of Technology\, China)
DTSTART:20250414T140000Z
DTEND:20250414T150000Z
DTSTAMP:20260404T110914Z
UID:QGS/126
DESCRIPTION:Title: A Theory of Locally Convex Hopf Algebras -- I. Basic Theory and Examp
les\nby Hua Wang (Harbin Institute of Technology\, China) as part of Q
uantum Groups Seminar [QGS]\n\n\nAbstract\nThis is the first of two talks
on a recent theory of locally convex Hopf algebras. After a brief introduc
tion to some relevant facts on locally convex spaces as well as their topo
logical tensor products\, we will describe the main theory with an emphasi
s on duality. We will see that besides the usual strong dual\, the theory
encompasses naturally a new type of dual called the polar dual. After pres
enting the main theoretical results\, we will illustrate the theory with v
arious examples. In particular\, we will see how to resolve the duality pr
oblem for classical Hopf algebras\, how to describe a Lie group as well as
its dual using smooth functions\, and how to incorporate compact and disc
rete quantum groups into this framework.\n
LOCATION:https://stable.researchseminars.org/talk/QGS/126/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Roberto Hernández Palomares (University of Waterloo\, Canada)
DTSTART:20250317T150000Z
DTEND:20250317T160000Z
DTSTAMP:20260404T110914Z
UID:QGS/127
DESCRIPTION:Title: Quantum graphs\, subfactors and tensor categories\nby Roberto Her
nández Palomares (University of Waterloo\, Canada) as part of Quantum Gro
ups Seminar [QGS]\n\n\nAbstract\nWe will introduce equivariant graphs with
respect to a quantum symmetry along with examples such as classical graph
s\, Cayley graphs of finite groupoids\, and their quantum analogues. These
graphs can be presented concretely by modeling a quantum vertex set by an
inclusion of operator algebras and the quantum edge set by an equivariant
endomorphism\, idempotent with respect to convolution/Schur product. Equi
pped with this viewpoint and tools from subfactor theory\, we will see how
to obtain all these idempotents using higher relative commutants and the
quantum Fourier transform. Finally\, we will state a quantum version of Fr
ucht's Theorem\, showing that every quasitriangular finite quantum groupoi
d arises as certain automorphisms of some categorified graph.\n
LOCATION:https://stable.researchseminars.org/talk/QGS/127/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sang-Gyun Youn (Seoul National University\, South Korea)
DTSTART:20250331T080000Z
DTEND:20250331T090000Z
DTSTAMP:20260404T110914Z
UID:QGS/128
DESCRIPTION:Title: A Khintchine inequality for central Fourier series on non-Kac compact
quantum groups\nby Sang-Gyun Youn (Seoul National University\, South
Korea) as part of Quantum Groups Seminar [QGS]\n\n\nAbstract\nThe study of
Khintchine inequalities has a long history in abstract harmonic analysis.
While there is almost no possibility of non-trivial Khintchine inequality
for central Fourier series on compact connected semisimple Lie groups\, i
t has turned out that a strong contrast holds within the framework of comp
act quantum groups. Specifically\, a Khintchine inequality with operator c
oefficients is proved for arbitrary central Fourier series in a large clas
s of non-Kac compact quantum groups. The main examples include the Drinfel
d-Jimbo q-deformations\, the free orthogonal quantum groups\, and the quan
tum automorphism groups.\n
LOCATION:https://stable.researchseminars.org/talk/QGS/128/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Heon Lee (Harbin Institute of Technology\, China)
DTSTART:20250407T120000Z
DTEND:20250407T130000Z
DTSTAMP:20260404T110914Z
UID:QGS/129
DESCRIPTION:Title: First-order differential calculi and Laplacians on $q$-deformations o
f compact semisimple Lie groups\nby Heon Lee (Harbin Institute of Tech
nology\, China) as part of Quantum Groups Seminar [QGS]\n\n\nAbstract\nIn
this talk\, we suggest a simple definition of Laplacian on a compact quant
um group (CQG) associated with a first-order differential calculus (FODC)
on it. Applied to the classical differential calculus on a compact Lie gro
up\, this definition yields classical Laplacians\, as it should. Moreover\
, on the CQG $ K_q $ arising from the $ q $-deformation of a compact semis
imple Lie group $K$\, we can find many interesting linear operators that s
atisfy this definition\, which converge to a classical Laplacian on $ K $
as $ q $ tends to 1. In the light of this\, we call them $ q $-Laplacians
on $ K_q $ and investigate some of their operator theoretic properties. In
particlar\, we show that the heat semigroups generated by these are not c
ompletely positive\, suggesting that perhaps on the CQG $ K_q $\, stochast
ic processes that are most relevant to the geometry of it are not quantum
Markov processes. This work is based on the preprint arXiv:2410.00720.\n
LOCATION:https://stable.researchseminars.org/talk/QGS/129/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hua Wang (Harbin Institute of Technology\, China)
DTSTART:20250421T140000Z
DTEND:20250421T150000Z
DTSTAMP:20260404T110914Z
UID:QGS/130
DESCRIPTION:Title: A Theory of Locally Convex Hopf Algebras -- II. More Duality Results
and Examples\nby Hua Wang (Harbin Institute of Technology\, China) as
part of Quantum Groups Seminar [QGS]\n\n\nAbstract\nThis is the second of
two talks on a recent theory of locally convex Hopf algebras. We will star
t by presenting a generalized version of the Gelfand duality\, and later a
pply it in various situations to obtain the underlying topological group f
rom the corresponding locally convex Hopf algebras. Surprisingly\, we can
go much beyond the locally compact case in this classical situation\, and
make the theory work for all topological groups with compactly generated t
opology. Then we shift to some categorical considerations\, allowing us to
obtain new topological quantum groups as well as their dualities that see
m not in the locally compact framework of Kustermans-Vaes. If time permits
\, we will conclude by mentionning how some deep structural results relate
d to Hilbert's fifth problem can be applied in this theory.\n
LOCATION:https://stable.researchseminars.org/talk/QGS/130/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Farrokh Razavinia (Institute for Research in Fundamental Sciences\
, Iran)
DTSTART:20250519T140000Z
DTEND:20250519T150000Z
DTSTAMP:20260404T110914Z
UID:QGS/131
DESCRIPTION:Title: C*-graph algebras and beyond\nby Farrokh Razavinia (Institute for
Research in Fundamental Sciences\, Iran) as part of Quantum Groups Semina
r [QGS]\n\n\nAbstract\nGraph C*-algebras have shown their importance in ma
thematics and other disciplines. For instance\, recall the theory of quant
um groups and quantum graphs\, they can provide us with required structure
s in proving or disproving some interrelated problems. For example\, in ou
r recent papers\, we showed their importance in looking at some very well-
known wonder questions in mathematics from a different direction. In this
talk\, we will present some elementary definitions and results concerning
graph C*-algebras\, and then we will try to study some constructive exampl
es\, and after that we will take a look at the concept of C*-colored graph
algebras\, and finally we will see how these structures will help us to m
ove into some very abstract mathematical object!\n
LOCATION:https://stable.researchseminars.org/talk/QGS/131/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kenny De Commer (Vrije Universiteit Brussel\, Belgium)
DTSTART:20251103T150000Z
DTEND:20251103T160000Z
DTSTAMP:20260404T110914Z
UID:QGS/132
DESCRIPTION:Title: Braided tensor product of von Neumann algebras\nby Kenny De Comme
r (Vrije Universiteit Brussel\, Belgium) as part of Quantum Groups Seminar
[QGS]\n\n\nAbstract\nWork of Meyer\, Roy and Woronowicz has shown that th
e category of C*-algebras with an action by a quasi-triangular quantum gro
up admits a monoidal structure by means of a braided tensor product. We ha
ve shown that a similar result holds if instead we work with actions on vo
n Neumann algebras. Moreover\, particular to this setting\, we are able to
show how (part of the) modular theory of a braided tensor product behaves
. We will frame the latter result in a more general setting of cocycle def
ormations. This is joint work with J. Krajczok.\n
LOCATION:https://stable.researchseminars.org/talk/QGS/132/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joeri De Ro (IMPAN\, Poland)
DTSTART:20251110T150000Z
DTEND:20251110T160000Z
DTSTAMP:20260404T110914Z
UID:QGS/133
DESCRIPTION:Title: Equivariant Eilenberg-Watts theorems for locally compact quantum grou
ps\nby Joeri De Ro (IMPAN\, Poland) as part of Quantum Groups Seminar
[QGS]\n\n\nAbstract\nGiven actions of a locally compact quantum group $G$
on the von Neumann algebras $A$ and $B$\, we can associate to it the categ
ory $\\operatorname{Corr}^G(A\,B)$ of G-A-B-correspondences. Special cases
of this category include the category $\\operatorname{Rep}(A)$ of unital\
, normal $*$-representations of $A$ on Hilbert spaces and the category $\\
operatorname{Rep}^G(A)$ of unital\, normal\, $G$-representations on Hilber
t spaces. We construct actions $\\operatorname{Rep}^G(A)\\curvearrowleft \
\operatorname{Rep}(G)$ and $\\operatorname{Rep}(A)\\curvearrowleft \\opera
torname{Rep}(\\hat{G})$\, providing us with natural examples of module cat
egories. We show that the categories of module functors $\\operatorname{Re
p}(B)\\to \\operatorname{Rep}(A)$ and \n$\\operatorname{Rep}^G(B)\\to \\op
eratorname{Rep}^G(A)$ are both equivalent to the category of $G$-$A$-$B$-c
orrespondences\, providing equivariant versions of the von Neumann algebra
ic Eilenberg-Watts theorem.\n
LOCATION:https://stable.researchseminars.org/talk/QGS/133/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Milan Donvil (École normale supérieure - PSL\, France)
DTSTART:20251117T150000Z
DTEND:20251117T160000Z
DTSTAMP:20260404T110914Z
UID:QGS/134
DESCRIPTION:Title: W*-superrigidity for discrete quantum groups\nby Milan Donvil (É
cole normale supérieure - PSL\, France) as part of Quantum Groups Seminar
[QGS]\n\n\nAbstract\nA (countable) group is called W*-superrigid if it is
completely remembered by its group von Neumann algebra in the following s
ense: if another group gives rise to an isomorphic group von Neumann algeb
ra\, the groups must be isomorphic. In the past fifteen years\, several cl
asses of W*-superrigid groups have been found. However\, it turns out that
many of these groups are not W*-superrigid in the larger class of compact
quantum groups: their group von Neumann algebras admit different quantum
group structures. In a recent work with Stefaan Vaes\, we found the first
examples of compact quantum groups which are 'quantum W*-superrigid'. To o
btain quantum W*-superrigidity\, we had to combine three different types o
f results: vanishing of cohomology\, rigidity of (quantum) groups relative
to a family of (quantum) group automorphisms\, and deformation/rigidity t
heory. I will explain why each of these three parts is essential and how t
hey come together to prove our main result.\n
LOCATION:https://stable.researchseminars.org/talk/QGS/134/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Leandro Vendramin (Vrije Universiteit Brussel\, Belgium)
DTSTART:20251124T150000Z
DTEND:20251124T160000Z
DTSTAMP:20260404T110914Z
UID:QGS/135
DESCRIPTION:Title: Nichols algebras over (solvable) groups\nby Leandro Vendramin (Vr
ije Universiteit Brussel\, Belgium) as part of Quantum Groups Seminar [QGS
]\n\n\nAbstract\nNichols algebras appear in various areas of mathematics\,
ranging from Hopf algebras and quantum groups to Schubert calculus and co
nformal field theory. In this talk\, I will review the main challenges in
classifying Nichols algebras over groups and discuss some recent classific
ation theorems. In particular\, I will highlight a recent classification r
esult (https://arxiv.org/abs/2411.02304)\, achieved in collaboration with
Andruskiewitsch and Heckenberger\, concerning finite-dimensional Nichols a
lgebras over solvable groups.\n
LOCATION:https://stable.researchseminars.org/talk/QGS/135/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Jaklitsch (University of Oslo\, Norway)
DTSTART:20251216T150000Z
DTEND:20251216T160000Z
DTSTAMP:20260404T110914Z
UID:QGS/136
DESCRIPTION:Title: The braided monoidal structure of tube algebra representations\nb
y David Jaklitsch (University of Oslo\, Norway) as part of Quantum Groups
Seminar [QGS]\n\n\nAbstract\nOcneanu's tube algebra plays a central role i
n lattice models of Levin-Wen type\, where topological excitations are giv
en by irreducible representations. The purpose of the talk is to report on
our recent results explicitly describing the tensor product of tube algeb
ra representations and the braiding. The well-known linear equivalence bet
ween tube algebra representations and the Drinfeld center category is (by
means of this structure) upgraded to a braided monoidal equivalence. This
is joint work with Makoto Yamashita.\n
LOCATION:https://stable.researchseminars.org/talk/QGS/136/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jennifer Brown (University of Edinburgh\, UK)
DTSTART:20260119T150000Z
DTEND:20260119T160000Z
DTSTAMP:20260404T110914Z
UID:QGS/137
DESCRIPTION:Title: Parabolic Reduction and Quantum Character Varieties\nby Jennifer
Brown (University of Edinburgh\, UK) as part of Quantum Groups Seminar [QG
S]\n\n\nAbstract\nCharacter varieties parametrise G-local systems on topol
ogical spaces\, for G a reductive group. They play a central role in physi
cal models such as Chern-Simons theory and have been widely studied. Many
constructions involving character varieties can be formulated with a combi
nation of skein theory and parabolic reduction along a Borel subgroup of G
.\n\nWe'll tell this story\, with the guiding goal of defining quantum clu
ster coordinates on quantised character varieties. This is based on joint
work with David Jordan.\n
LOCATION:https://stable.researchseminars.org/talk/QGS/137/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ben Gui (Tsinghua University\, China)
DTSTART:20260126T080000Z
DTEND:20260126T090000Z
DTSTAMP:20260404T110914Z
UID:QGS/138
DESCRIPTION:Title: Comparison of extensions of unitary VOAs and conformal nets\nby B
en Gui (Tsinghua University\, China) as part of Quantum Groups Seminar [QG
S]\n\n\nAbstract\nIn 2015\, Carpi-Kawahigashi-Longo-Weiner (CKLW) initiate
d a systematic study of the relationship between unitary vertex operator a
lgebras (UVOAs) and conformal nets (CNs). Building on their framework and
Wassermann’s computation of the Connes fusion of modules of loop group S
U(N) at positive integer levels\, I showed in 2018 and 2020 that many rati
onal UVOAs (including all WZW models) and their corresponding CNs have uni
tarily equivalent representation categories.\n\nIn this talk\, I will show
that when one considers extensions of UVOAs and CNs\, the abstract equiva
lence of representation categories arising from the theory of Frobenius al
gebras and Q-systems is compatible with the unitary equivalences (in the l
ine of CKLW and Wassermann) mentioned above.\n
LOCATION:https://stable.researchseminars.org/talk/QGS/138/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alfons Van Daele (KU Leuven\, Belgium)
DTSTART:20260413T140000Z
DTEND:20260413T150000Z
DTSTAMP:20260404T110914Z
UID:QGS/139
DESCRIPTION:Title: Discrete quantum groups\nby Alfons Van Daele (KU Leuven\, Belgium
) as part of Quantum Groups Seminar [QGS]\n\n\nAbstract\nDiscrete quantum
groups were first introduced as the duals of compact quantum groups in a
paper by Podleś and Woronowicz (1990). Later they were studied independen
tly by Effros and Ruan (1994) and myself (1996). All of this was done befo
re the duality of multiplier Hopf algebras with integrals was developed (1
998)\, as a special and motivating case of the theory of locally compact
quantum groups\, developed even later (2000).\n\nUnfortunately\, also in
more recent work\, discrete quantum groups have still been treated as dual
s of compact quantum groups and not as a concept of its own.\n\nIn this ta
lk I will discuss a somewhat updated version of the theory of discrete qua
ntum groups. Given a discrete quantum group $(A\,\\Delta)$\, I will focus
on the properties of $\\Delta(h)$ where $h$ is the cointegral. The element
$\\Delta(h)$ is a \\emph{separability idempotent} in the multiplier algeb
ra $M(A\\otimes A)$ carrying all the essential information about the disc
rete quantum group. \n\nI plan to use the discrete quantum group that aris
es from the Jimbo deformation of the enveloping algebra of the Lie algebra
of $SU(2)$ to illustrate some of the notions and properties of general di
screte quantum groups.\n
LOCATION:https://stable.researchseminars.org/talk/QGS/139/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Keshab Bakshi (IIT Kanpur\, India)
DTSTART:20260330T140000Z
DTEND:20260330T150000Z
DTSTAMP:20260404T110914Z
UID:QGS/141
DESCRIPTION:Title: Weak quantum hypergroups from finite index $C^*$-inclusions\nby K
eshab Bakshi (IIT Kanpur\, India) as part of Quantum Groups Seminar [QGS]\
n\n\nAbstract\nWe study finite index inclusions $B \\subset A$ of simple u
nital $C^*$-algebras and investigate the quantum symmetries arising from t
heir relative commutants. Using the convolution structure on higher relati
ve commutants\, we construct a canonical completely positive coproduct on
the second relative commutant $B^{\\prime} \\cap A_1$\, which gives it a n
atural coalgebra structure. This leads to the notion of a weak quantum hyp
ergroup. We show that such a structure arises canonically from any finite
index inclusion. In the irreducible case it becomes a quantum hypergroup\,
while in the depth $2$ case it recovers the weak Hopf algebra associated
with the inclusion. This is a joint work with Debashish Goswami and Bipl
ab Pal\n
LOCATION:https://stable.researchseminars.org/talk/QGS/141/
END:VEVENT
BEGIN:VEVENT
SUMMARY:TBA
DTSTART:20260427T140000Z
DTEND:20260427T150000Z
DTSTAMP:20260404T110914Z
UID:QGS/142
DESCRIPTION:by TBA as part of Quantum Groups Seminar [QGS]\n\nAbstract: TB
A\n
LOCATION:https://stable.researchseminars.org/talk/QGS/142/
END:VEVENT
END:VCALENDAR