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SUMMARY:Martijn Caspers (TU Delft)
DTSTART:20200825T114500Z
DTEND:20200825T130000Z
DTSTAMP:20260404T111246Z
UID:AnalyseFonctionnelle/1
DESCRIPTION:Title: Weak type estimates for multiple operator integrals an
d generalized absolute value functions\nby Martijn Caspers (TU Delft)
as part of Séminaire d’Analyse Fonctionnelle de l'UFC\n\n\nAbstract\nTh
is talk is concerned with the following question. Let $f$ be an $n$ times
differentiable function on the reals with bounded $n$-th derivative. Let $
f_n$ be its $n$-th order divided difference function. For instance $f_1(s\
,t) = (f(s) - f(t))/(s-t)$. Is it true that the multiple operator integral
$T_{f_n}$ maps $S_{p_1} \\times \\cdots \\times S_{p_n}$ to $S_{1\,\\inft
y}$ boundedly? Here $S_p$ is the Schatten non-commutative $L_p$-space and
$S_{1\,\\infty}$ is the non-commutative weak $L_1$ space. In case $n=1$ th
e question boils down on whether the Schur multiplier with symbol $(f_1(s\
,t))_{s\,t}$ is bounded from $S_1$ to $S_{1\,\\infty}$. We give a positive
answer to a class of functions involving the function $a(t)= \\mathrm{sig
n}(t) t^n$. If $n =1$ we find a complete solution and the answer is affirm
ative. We give further details and definitions in the talk\, including the
theory of multiple operator integrals. This is joint work with Fedor Suko
chev\, Dima Zanin as well as Denis Potapov.\n\nEmail uwe.franz@univ-fcomte
.fr for the link.\n
LOCATION:https://stable.researchseminars.org/talk/AnalyseFonctionnelle/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jacek Krajczok (IMPAN)
DTSTART:20200908T114500Z
DTEND:20200908T130000Z
DTSTAMP:20260404T111246Z
UID:AnalyseFonctionnelle/2
DESCRIPTION:Title: Type I locally compact quantum groups: coamenability a
nd applications\nby Jacek Krajczok (IMPAN) as part of Séminaire d’A
nalyse Fonctionnelle de l'UFC\n\n\nAbstract\nWe say that a locally compact
quantum group is type I if its universal C$^*$ algebra (which is equal to
$C^u_0(\\hat{G})$) is type I. This class of quantum groups can be though
of as an intermediate step between compact and general locally compact qua
ntum groups\; they are significantly more general than compact ones\, but
still have tractable representation theory. Similarly to the compact case\
, one can define "character-like" operators associated with suitable repre
sentations. I will discuss a result which states that coamenability of G i
s equivalent to a certain condition on spectra of these operators. If time
permits\, I will also discuss how one can use theory of type I locally co
mpact quantum groups to show that the quantum space underlying the Toeplit
z algebra does not admit a quantum group structure (joint work with Piotr
Sołtan).\n\nEmail uwe.franz@univ-fcomte.fr for the link.\n
LOCATION:https://stable.researchseminars.org/talk/AnalyseFonctionnelle/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Biswarup Das
DTSTART:20200922T114500Z
DTEND:20200922T130000Z
DTSTAMP:20260404T111246Z
UID:AnalyseFonctionnelle/3
DESCRIPTION:Title: Towards quantizing separate continuity: A quantum ver
sion of Ellis joint continuity theorem\nby Biswarup Das as part of Sé
minaire d’Analyse Fonctionnelle de l'UFC\n\n\nAbstract\nLet $S$ be a top
ological space\, which is also a semigroup with identity\, such that the m
ultiplication is separately continuous. Such semigroups are called semitop
ological semigroups. These type of objects occur naturally\, if onestudies
weakly almost periodic compactification of a topological group. Now if we
assume the following: (a) The topology of $S$ is locally compact. (b) Abs
tract algebraically speaking\, $S$ is a group (i.e. every element has an i
nverse). (c) The multiplication is separately continuous as above (no othe
r assumption. This is the only assumption concerning the interaction of th
e topology with the group structure). Then it follows that S becomes a top
ological group i.e.: (a) The multiplication becomes jointly continuous. (b
) The inverse is also continuous. This extremely beautiful fact was proven
by R. Ellis in 1957 and is known in the literature as Ellis joint continu
ity theorem. In this talk\, we will prove a non-commutative version of thi
s result. Upon briefly reviewing the notion of semitopological semigroup\,
we will introduce ''compact semitopological quantum semigroup'' which wer
e before introduced by M. Daws in 2014 as a tool to study almost periodici
ty of Hopf von Neumann algebras. Then we will give a necessary and suffici
ent condition on these objects\, so that they become a compact quantum gro
up. As a corollary\, we will give a new proof of the Ellis joint continuit
y theorem as well. This is the joint work with Colin Mrozinski.\n\nPlease
contact uwe.franz@univ-fcomte.fr for the link.\n
LOCATION:https://stable.researchseminars.org/talk/AnalyseFonctionnelle/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jonas Wahl (Hausdorff Center for Mathematics\, Bonn)
DTSTART:20201020T114500Z
DTEND:20201020T130000Z
DTSTAMP:20260404T111246Z
UID:AnalyseFonctionnelle/4
DESCRIPTION:Title: Markov dynamics on branching graphs of diagram algebra
s\nby Jonas Wahl (Hausdorff Center for Mathematics\, Bonn) as part of
Séminaire d’Analyse Fonctionnelle de l'UFC\n\n\nAbstract\nThoma's famou
s theorem on the classification of characters on the infinite symmetric gr
oup has been very influential in different areas of mathematics such as co
mbinatorics and probability theory. In this talk\, we explain versions of
Thoma's theorem for different diagram algebras arising out of subfactor th
eory and Banica and Speicher's theory of easy quantum groups. As Thoma's c
lassical theorem\, these results can be formulated in a probabilistic lang
uage and we find interesting new connections to random lattice paths and r
andom walks on trees.\n\nPlease contact uwe.franz@univ-fcomte.fr for the l
ink (it is same link as the previous seminar).\n
LOCATION:https://stable.researchseminars.org/talk/AnalyseFonctionnelle/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Brannan (Texas A&M University)
DTSTART:20210223T150000Z
DTEND:20210223T160000Z
DTSTAMP:20260404T111246Z
UID:AnalyseFonctionnelle/5
DESCRIPTION:Title: Complete logarithmic Sobolev inequalities and non-comm
utative Ricci curvature\nby Michael Brannan (Texas A&M University) as
part of Séminaire d’Analyse Fonctionnelle de l'UFC\n\n\nAbstract\nI wil
l give a brief introduction to the study of log-Sobolev type inequalities
(LSI's) for quantum Markov semigroups and some of their applications. In
the context of classical heat semigroups on compact Riemannian manifolds\,
the famous Bakry-Emery theorem provides a beautiful connection between th
e geometry of the underlying manifold and the LSI\, showing that a positiv
e lower bound on the Ricci curvature implies an LSI for the heat semigroup
. I will discuss an information-theoretic approach to obtain modified log
-Sobolev inequalities based on non-positive non-commutative Ricci curvatur
e lower bounds previously developed by Carlen and Maas. Using these tools
\, we are able to find new examples of quantum Markov semigroups satisfyin
g a completely bounded version of the modified LSI\, including heat semigr
oups on free quantum groups. This talk is based on joint work with Li Gao
(TUM) and Marius Junge (UIUC).\n\nPlease contact uwe.franz@univ-fcomte.fr
for the link (it is same link as the previous seminar).\n
LOCATION:https://stable.researchseminars.org/talk/AnalyseFonctionnelle/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ryosuki Sato (Nagoya University)
DTSTART:20210309T124500Z
DTEND:20210309T140000Z
DTSTAMP:20260404T111246Z
UID:AnalyseFonctionnelle/6
DESCRIPTION:Title: Markov dynamics on unitary duals of compact quantum gr
oups\nby Ryosuki Sato (Nagoya University) as part of Séminaire d’An
alyse Fonctionnelle de l'UFC\n\n\nAbstract\nIn this talk\, we will discuss
Markov semigroups on unitary duals (i.e.\, the set of all irreducible rep
resentations) of compact quantum groups. First\, we will construct quantum
Markov semigroups on the group von Neumann algebra of compact quantum gro
up based on its Hopf-algebra structure and characters of the compact quant
um group. Then we will show the dynamics preserve the center of the group
von Neumann algebra\, and it gives the dynamics on the unitary dual. Moreo
ver\, the dynamics have generators\, and we can describe it explicitly by
the representation theory. In particular\, we will deal with the case of q
uantum unitary groups.\n\nPlease contact uwe.franz@univ-fcomte.fr for the
link (it is same link as the previous seminar).\n
LOCATION:https://stable.researchseminars.org/talk/AnalyseFonctionnelle/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fabio Cipriani (Politecnico di Milano)
DTSTART:20210511T114500Z
DTEND:20210511T130000Z
DTSTAMP:20260404T111246Z
UID:AnalyseFonctionnelle/7
DESCRIPTION:Title: On a noncommutative Sierpiński gasket\nby Fabio C
ipriani (Politecnico di Milano) as part of Séminaire d’Analyse Fonction
nelle de l'UFC\n\n\nAbstract\nWe illustrate the construction of a C*-algeb
ra A that can be genuinely interpreed as a quantization of the classical S
ierpiński gasket\, the most studied instance of a self-similar fractal sp
ace. We further describe the discrete and continuous spectrum of A\, the s
tructure of the traces on A as well as the construction of a Dirichlet for
m E and of a spectral triple (A\,D\,H).\n\nPlease contact uwe.franz@univ-f
comte.fr for the link (it is same link as the previous seminar).\n
LOCATION:https://stable.researchseminars.org/talk/AnalyseFonctionnelle/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Kyed (University of Southern Denmark)
DTSTART:20210525T114500Z
DTEND:20210525T130000Z
DTSTAMP:20260404T111246Z
UID:AnalyseFonctionnelle/8
DESCRIPTION:Title: The Podleś spheres converge to the sphere\nby Dav
id Kyed (University of Southern Denmark) as part of Séminaire d’Analyse
Fonctionnelle de l'UFC\n\n\nAbstract\nThe Podleś spheres\, which are q-d
eformed analogues of the 2-sphere\, are by now among the most classical ob
jects in non-commutative geometry\, but only recently their structure as n
on-commutative Riemannian manifolds has begun to unravel. In my talk\, I w
ill first provide an introduction to Rieffel’s notion of compact quantum
metric spaces and his non-commutative counterpart to the Gromov-Hausdorff
distance\, and then present some recent progress within this field which
shows that the quantised 2-spheres actually converge (in the quantum Gromo
v-Hausdorff distance) to the classical round 2-sphere as the deformation p
arameter q tends to 1. The talk is based on joint works with Konrad Aguila
r and Jens Kaad.\n\nPlease contact uwe.franz@univ-fcomte.fr for the link (
it is same link as the previous seminar).\n
LOCATION:https://stable.researchseminars.org/talk/AnalyseFonctionnelle/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Haonan Zhang (IST Austria)
DTSTART:20210608T114500Z
DTEND:20210608T130000Z
DTSTAMP:20260404T111246Z
UID:AnalyseFonctionnelle/9
DESCRIPTION:Title: Curvature-dimension conditions for symmetric quantum M
arkov semigroups\nby Haonan Zhang (IST Austria) as part of Séminaire
d’Analyse Fonctionnelle de l'UFC\n\n\nAbstract\nThe curvature-dimension
condition consists of the lower Ricci curvature bound and upper dimension
bound of the Riemannian manifold\, which has a number of geometric consequ
ences and is very helplful in proving many functional inequalities. In thi
s talk I will speak about two noncommutative versions of curvature-dimensi
on bounds for symmetric quantum Markov semigroups over matrix algebras. Un
der suitable such curvature-dimension conditions\, we prove a family of di
mension-dependent functional inequalities\, a version of the Bonnet-Myers
theorem and concavity of entropy power in the noncommutative setting. We a
lso provide examples satisfying certain curvature-dimension conditions\, i
ncluding Schur multipliers over matrix algebras\, Herz-Schur multipliers o
ver group algebras and depolarizing semigroups. Joint work with Melchior W
irth (IST Austria).\n\nPlease contact uwe.franz@univ-fcomte.fr for the lin
k (it is same link as the previous seminar).\n
LOCATION:https://stable.researchseminars.org/talk/AnalyseFonctionnelle/9/
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