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BEGIN:VEVENT
SUMMARY:Orr Shalit (Technion)
DTSTART:20210802T140000Z
DTEND:20210802T145000Z
DTSTAMP:20260404T041641Z
UID:CMO-21w5124/1
DESCRIPTION:Title: Davidson and Kennedy’s take on noncommutative convexity\n
by Orr Shalit (Technion) as part of CMO workshop: Multivariable Operator
Theory and Function Spaces in several Variables\n\n\nAbstract\nI will pres
ent Davidson and Kennedy’s theory of noncommutative convexity and noncom
mutative Choquet theory\, which appeared in a preprint two years ago. I wi
ll compare to older notions of convexity\, such as matrix convexity\, and
illustrate what it can do for us.\n
LOCATION:https://stable.researchseminars.org/talk/CMO-21w5124/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Jury (University of Florida)
DTSTART:20210802T150500Z
DTEND:20210802T155500Z
DTSTAMP:20260404T041641Z
UID:CMO-21w5124/2
DESCRIPTION:Title: Geometry of free loci and factorization of noncommutative polyn
omials (Helton\, Klep\, Volčič)\nby Michael Jury (University of Flor
ida) as part of CMO workshop: Multivariable Operator Theory and Function
Spaces in several Variables\n\n\nAbstract\nWe will discuss the paper of He
lton\, Klep\, and Volčič with this title (and present some relevant back
ground). It concerns the zero locus of a noncommutative polynomial. If p i
s a noncommutative polynomial in d variables\, its zero locus is defined t
o be the set of d-tuples of square matrices X\, of all sizes\, for which d
et(p(X))=0. It is proved (among other things) that p is irreducible if and
only if the zero locus (at size n) is an irreducible variety for sufficie
ntly large n. A key step in the proof is an irreducibility result for line
ar pencils.\n
LOCATION:https://stable.researchseminars.org/talk/CMO-21w5124/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yi Wang (Vanderbilt University)
DTSTART:20210802T161500Z
DTEND:20210802T170500Z
DTSTAMP:20260404T041641Z
UID:CMO-21w5124/3
DESCRIPTION:Title: The Drury-Arveson space as an L2 space defined by a distributio
n\nby Yi Wang (Vanderbilt University) as part of CMO workshop: Multiv
ariable Operator Theory and Function Spaces in several Variables\n\n\nAbst
ract\nI will try to discuss some of the basic properties of the Drury-Arve
son space from a different point of view: that is\, to view the Drury Arve
son space as an analytic function space that is $L^2$ integrable with a di
stribution. This is based on several papers by Shalit\, Arcozzi\, Rochberg
\, Sawyer\, etc\n
LOCATION:https://stable.researchseminars.org/talk/CMO-21w5124/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Adam Dor-On (University of Copenhagen)
DTSTART:20210803T140000Z
DTEND:20210803T145000Z
DTSTAMP:20260404T041641Z
UID:CMO-21w5124/4
DESCRIPTION:Title: Blaschke-Singular-Outer factorization for analytic free functio
ns on the nc unit ball\nby Adam Dor-On (University of Copenhagen) as p
art of CMO workshop: Multivariable Operator Theory and Function Spaces in
several Variables\n\n\nAbstract\nA classical result of Herglotz and F. Ri
esz says that any bounded holomorphic function on the unit disk admits a f
actorization into a product of an inner Blaschke product\, an inner singul
ar function and an outer function. We will discuss an extension of this re
sult\, due to Jury\, Martin and Shamovich\, to free analytic functions on
the non-commutative unit ball. Time permitting\, we will showcase some exa
mples coming from nc rational functions.\n
LOCATION:https://stable.researchseminars.org/talk/CMO-21w5124/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nikolaos Chalmoukis (University of Bologna)
DTSTART:20210803T150500Z
DTEND:20210803T155500Z
DTSTAMP:20260404T041641Z
UID:CMO-21w5124/5
DESCRIPTION:Title: Hardy Sobolev spaces in several complex variables\nby Nikol
aos Chalmoukis (University of Bologna) as part of CMO workshop: Multivari
able Operator Theory and Function Spaces in several Variables\n\n\nAbstrac
t\nThe class of Hardy Sobolev spaces in the unit ball of C^n is a family o
f spaces including the Hardy\, Drury Arveson\, Bergman and Dirichlet space
. In this talk we will focus on questions such as characterization of mult
ipliers\, interpolating sequences and exceptional sets\, mostly presenting
earlier work of Ahern\, Work\, Verbitsky and others. \nIn particular we f
ind that a common factor of all these problems is an abstract potential th
eory due to Adams and Hedberg adapted to the setting of Hardy Sobolev spac
es. \nWe shall make an effort to highlight the limitations of the techniqu
es that have been used so far and present some open problems that might be
of interest.\n
LOCATION:https://stable.researchseminars.org/talk/CMO-21w5124/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kelly Bickel (Bucknell University)
DTSTART:20210803T161500Z
DTEND:20210803T170500Z
DTSTAMP:20260404T041641Z
UID:CMO-21w5124/6
DESCRIPTION:Title: Pascoe’s NC Free Universal Monodromy Theorem and Applications
\nby Kelly Bickel (Bucknell University) as part of CMO workshop: Mult
ivariable Operator Theory and Function Spaces in several Variables\n\n\nAb
stract\nA crucial assumption of the classical monodromy theorem states tha
t the underlying domain must be simply connected. Recent work by J.E. Pasc
oe has established the surprising fact that\, in the non-commutative free
setting\, “simply connected” can be replaced with merely “connected.
” This talk is based on Pascoe’s associated paper “Non-commutative F
ree Universal Monodromy\, Pluriharmonic Conjugates\, and Plurisubharmonici
ty” and will provide both the geometric intuition behind his monodromy t
heorem as well as a number of interesting applications.\n
LOCATION:https://stable.researchseminars.org/talk/CMO-21w5124/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eli Shamovich (Ben-Gurion University)
DTSTART:20210805T140000Z
DTEND:20210805T145000Z
DTSTAMP:20260404T041641Z
UID:CMO-21w5124/7
DESCRIPTION:Title: Residual finite-dimensionality for operator algebras\nby El
i Shamovich (Ben-Gurion University) as part of CMO workshop: Multivariabl
e Operator Theory and Function Spaces in several Variables\n\n\nAbstract\n
In this talk\, I will present the works of Clouatre and Dor-On and Clouatr
e and Ramsey. These works define and study residual finite-dimensionality
for non-self-adjoint operator algebras. In particular\, we will explore th
e residual finite-dimensionality of the maximal C^*-cover of an RFD operat
or algebra. I will connect these notions to noncommutative function theory
. Time permitting\, I will discuss the notion of coactions of semigroups o
n operator algebras\, and in particular\, RFD coactions.\n
LOCATION:https://stable.researchseminars.org/talk/CMO-21w5124/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alberto Dayan (Washington University in St. Louis)
DTSTART:20210805T150500Z
DTEND:20210805T155500Z
DTSTAMP:20260404T041641Z
UID:CMO-21w5124/8
DESCRIPTION:Title: Interpolating d-tuples of matrices\nby Alberto Dayan (Washi
ngton University in St. Louis) as part of CMO workshop: Multivariable Ope
rator Theory and Function Spaces in several Variables\n\n\nAbstract\nThe m
ain goal of the talk is to give an overview of some known arguments that r
elates interpolating sequences in a multi-variable setting to Riesz system
type conditions on reproducing kernel Hilbert spaces. The first part of t
he talk reviews Agler’s and McCarthy’s characterization of interpolati
ng sequences in the bidisc\, and it highlights how some of those technique
s apply also to a generalized interpolating problem\, in which the nodes a
re d-tuples of commuting square matrices (of any dimension).\nThe second p
art of the talk deals with the case of sequences of eventually non commuti
ng matrices. We review the robust theory of noncommutative function theory
on the noncommutative unit ball\, and we see how a noncommutative version
of the Pick property enjoyed by the NC Drury-Arveson space gives a charac
terization of interpolating sequences in this non commutative setting.\n
LOCATION:https://stable.researchseminars.org/talk/CMO-21w5124/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Greg Knese (Washington University in St. Louis)
DTSTART:20210805T161500Z
DTEND:20210805T170500Z
DTSTAMP:20260404T041641Z
UID:CMO-21w5124/9
DESCRIPTION:Title: Singularities of rational inner functions in higher dimensions
(Bickel\, Pascoe\, Sola)\nby Greg Knese (Washington University in St.
Louis) as part of CMO workshop: Multivariable Operator Theory and Functio
n Spaces in several Variables\n\n\nAbstract\nWe study the boundary behavio
r of rational inner functions (RIFs) in dimensions three and higher from b
oth analytic and geometric viewpoints. On the analytic side\, we use the c
ritical integrability of the derivative of a rational inner function of se
veral variables to quantify the behavior of a RIF near its singularities\,
and on the geometric side we show that the unimodular level sets of a RIF
convey information about its set of singularities. We then specialize to
three-variable degree (m\,n\,1) RIFs and conduct a detailed study of their
derivative integrability\, zero set and unimodular level set behavior\, a
nd non-tangential boundary values. Our results\, coupled with construction
s of non-trivial RIF examples\, demonstrate that much of the nice behavior
seen in the two-variable case is lost in higher dimensions.\n
LOCATION:https://stable.researchseminars.org/talk/CMO-21w5124/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lukasz Kosinski (University in Krakow)
DTSTART:20210806T140000Z
DTEND:20210806T145000Z
DTSTAMP:20260404T041641Z
UID:CMO-21w5124/10
DESCRIPTION:Title: Theory of holomorphically invariant metrics in Nevalinna Pick
interpolation\nby Lukasz Kosinski (University in Krakow) as part of CM
O workshop: Multivariable Operator Theory and Function Spaces in several
Variables\n\n\nAbstract\nWe shall discuss some aspects of the theory of in
variant\nfunctions and their applications to Nevanlinna Pick interpolation
and\nextension problems\n
LOCATION:https://stable.researchseminars.org/talk/CMO-21w5124/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Dritschel (University of Newcastle)
DTSTART:20210806T150500Z
DTEND:20210806T155500Z
DTSTAMP:20260404T041641Z
UID:CMO-21w5124/11
DESCRIPTION:Title: Real Algebraic Geometry via Operator Theory\nby Michael Dr
itschel (University of Newcastle) as part of CMO workshop: Multivariable
Operator Theory and Function Spaces in several Variables\n\n\nAbstract\nRe
al algebraic geometry as a discipline was born out of Hilbert's 17th probl
em\, presented at the 1900 ICM. In it\, the primary goal is to succinctly
describe the set of polynomials which are non-negative on a semi-algebrai
c set (that is\, one described by a finite set of polynomial inequalities)
. Until the 1980s\, the field was predominantly studied via logic and alg
ebra. Konrad Schmüdgen then discovered a deep connection to analysis. M
ore recently\, analysts have focused on (freely) non-commutative versions
of the area's now classical problems. We emphasize the latter\, especiall
y a few key papers of Helton and McCullough\, along with some of the work
following on.\n
LOCATION:https://stable.researchseminars.org/talk/CMO-21w5124/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Raphaël Clouâtre (University of Manitoba)
DTSTART:20210806T161500Z
DTEND:20210806T170500Z
DTSTAMP:20260404T041641Z
UID:CMO-21w5124/12
DESCRIPTION:Title: The Ostermann--Ransford approach to the Crouzeix conjecture\nby Raphaël Clouâtre (University of Manitoba) as part of CMO workshop:
Multivariable Operator Theory and Function Spaces in several Variables\n
\n\nAbstract\nA theorem of Crouzeix implies that\, given a Hilbert space o
perator $T$\, its numerical range $W(T)$ is necessarily a spectral set. In
other words\, upon endowing the space of polynomials with the supremum no
rm over $W(T)$\, the functional calculus\n\\[\np\\mapsto p(T)\, \\quad p\\
in \\mathbb{C}[z]\n\\]\nis a bounded homomorphism. What is the norm of thi
s homomorphism?\n\nTo this day\, the precise answer is yet unknown\, altho
ugh in 2007 Crouzeix conjectured it to be at most $2$. In this talk\, I wi
ll describe a recent approach to the conjecture\, proposed by Ostermann an
d Ransford. Surprisingly\, this approach is very general and almost purely
algebraic: it is concerned with the interaction between finite-dimensiona
l representations and certain conjugate-linear self-maps of a uniform alg
ebra.\n
LOCATION:https://stable.researchseminars.org/talk/CMO-21w5124/12/
END:VEVENT
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