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SUMMARY:Martijn Caspers (TU Delft)
DTSTART;VALUE=DATE-TIME:20200825T114500Z
DTEND;VALUE=DATE-TIME:20200825T130000Z
DTSTAMP;VALUE=DATE-TIME:20210419T082226Z
UID:AnalyseFonctionnelle/1
DESCRIPTION:Title: Weak type estimates for multiple operator integrals and gener
alized absolute value functions\nby Martijn Caspers (TU Delft) as part
of Séminaire d’Analyse Fonctionnelle de l'UFC\n\n\nAbstract\nThis talk
is concerned with the following question. Let $f$ be an $n$ times differe
ntiable 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 $S_{1\,\\infty}$ bou
ndedly? 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 $n=1$ the quest
ion 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 $a(t)= \\mathrm{sign}(t) t
^n$. If $n =1$ we find a complete solution and the answer is affirmative.
We give further details and definitions in the talk\, including the theory
of multiple operator integrals. This is joint work with Fedor Sukochev\,
Dima Zanin as well as Denis Potapov.\n\nEmail uwe.franz@univ-fcomte.fr for
the link.\n
LOCATION:https://researchseminars.org/talk/AnalyseFonctionnelle/1/
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BEGIN:VEVENT
SUMMARY:Jacek Krajczok (IMPAN)
DTSTART;VALUE=DATE-TIME:20200908T114500Z
DTEND;VALUE=DATE-TIME:20200908T130000Z
DTSTAMP;VALUE=DATE-TIME:20210419T082226Z
UID:AnalyseFonctionnelle/2
DESCRIPTION:Title: Type I locally compact quantum groups: coamenability and appl
ications\nby Jacek Krajczok (IMPAN) as part of Séminaire d’Analyse
Fonctionnelle de l'UFC\n\n\nAbstract\nWe say that a locally compact quantu
m 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 a
n intermediate step between compact and general locally compact quantum gr
oups\; they are significantly more general than compact ones\, but still h
ave tractable representation theory. Similarly to the compact case\, one c
an define "character-like" operators associated with suitable representati
ons. I will discuss a result which states that coamenability of G is equiv
alent to a certain condition on spectra of these operators. If time permit
s\, I will also discuss how one can use theory of type I locally compact q
uantum groups to show that the quantum space underlying the Toeplitz algeb
ra 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://researchseminars.org/talk/AnalyseFonctionnelle/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Biswarup Das
DTSTART;VALUE=DATE-TIME:20200922T114500Z
DTEND;VALUE=DATE-TIME:20200922T130000Z
DTSTAMP;VALUE=DATE-TIME:20210419T082226Z
UID:AnalyseFonctionnelle/3
DESCRIPTION:Title: Towards quantizing separate continuity: A quantum version of
Ellis joint continuity theorem\nby Biswarup Das as part of Séminaire
d’Analyse Fonctionnelle de l'UFC\n\n\nAbstract\nLet $S$ be a topologica
l space\, which is also a semigroup with identity\, such that the multipli
cation is separately continuous. Such semigroups are called semitopologica
l 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) Abstract a
lgebraically speaking\, $S$ is a group (i.e. every element has an inverse)
. (c) The multiplication is separately continuous as above (no other assum
ption. This is the only assumption concerning the interaction of the topol
ogy with the group structure). Then it follows that S becomes a topologica
l group i.e.: (a) The multiplication becomes jointly continuous. (b) The i
nverse is also continuous. This extremely beautiful fact was proven by R.
Ellis in 1957 and is known in the literature as Ellis joint continuity the
orem. In this talk\, we will prove a non-commutative version of this resul
t. Upon briefly reviewing the notion of semitopological semigroup\, we wil
l introduce ''compact semitopological quantum semigroup'' which were befor
e introduced by M. Daws in 2014 as a tool to study almost periodicity of H
opf von Neumann algebras. Then we will give a necessary and sufficient con
dition on these objects\, so that they become a compact quantum group. As
a corollary\, we will give a new proof of the Ellis joint continuity theor
em as well. This is the joint work with Colin Mrozinski.\n\nPlease contact
uwe.franz@univ-fcomte.fr for the link.\n
LOCATION:https://researchseminars.org/talk/AnalyseFonctionnelle/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jonas Wahl (Hausdorff Center for Mathematics\, Bonn)
DTSTART;VALUE=DATE-TIME:20201020T114500Z
DTEND;VALUE=DATE-TIME:20201020T130000Z
DTSTAMP;VALUE=DATE-TIME:20210419T082226Z
UID:AnalyseFonctionnelle/4
DESCRIPTION:Title: Markov dynamics on branching graphs of diagram algebras\n
by Jonas Wahl (Hausdorff Center for Mathematics\, Bonn) as part of Sémina
ire d’Analyse Fonctionnelle de l'UFC\n\n\nAbstract\nThoma's famous theor
em on the classification of characters on the infinite symmetric group has
been very influential in different areas of mathematics such as combinato
rics and probability theory. In this talk\, we explain versions of Thoma's
theorem for different diagram algebras arising out of subfactor theory an
d Banica and Speicher's theory of easy quantum groups. As Thoma's classica
l theorem\, these results can be formulated in a probabilistic language an
d we find interesting new connections to random lattice paths and random w
alks on trees.\n\nPlease contact uwe.franz@univ-fcomte.fr for the link (it
is same link as the previous seminar).\n
LOCATION:https://researchseminars.org/talk/AnalyseFonctionnelle/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Brannan (Texas A&M University)
DTSTART;VALUE=DATE-TIME:20210223T150000Z
DTEND;VALUE=DATE-TIME:20210223T160000Z
DTSTAMP;VALUE=DATE-TIME:20210419T082226Z
UID:AnalyseFonctionnelle/5
DESCRIPTION:Title: Complete logarithmic Sobolev inequalities and non-commutative
Ricci curvature\nby Michael Brannan (Texas A&M University) as part of
Séminaire d’Analyse Fonctionnelle de l'UFC\n\n\nAbstract\nI will 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 con
text of classical heat semigroups on compact Riemannian manifolds\, the fa
mous Bakry-Emery theorem provides a beautiful connection between the geome
try of the underlying manifold and the LSI\, showing that a positive lower
bound on the Ricci curvature implies an LSI for the heat semigroup. I wi
ll discuss an information-theoretic approach to obtain modified log-Sobole
v inequalities based on non-positive non-commutative Ricci curvature lower
bounds previously developed by Carlen and Maas. Using these tools\, we a
re able to find new examples of quantum Markov semigroups satisfying a com
pletely bounded version of the modified LSI\, including heat semigroups 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 th
e link (it is same link as the previous seminar).\n
LOCATION:https://researchseminars.org/talk/AnalyseFonctionnelle/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ryosuki Sato (Nagoya University)
DTSTART;VALUE=DATE-TIME:20210309T124500Z
DTEND;VALUE=DATE-TIME:20210309T140000Z
DTSTAMP;VALUE=DATE-TIME:20210419T082226Z
UID:AnalyseFonctionnelle/6
DESCRIPTION:Title: Markov dynamics on unitary duals of compact quantum groups\nby Ryosuki Sato (Nagoya University) as part of Séminaire d’Analyse F
onctionnelle de l'UFC\n\n\nAbstract\nIn this talk\, we will discuss Markov
semigroups on unitary duals (i.e.\, the set of all irreducible representa
tions) of compact quantum groups. First\, we will construct quantum Markov
semigroups on the group von Neumann algebra of compact quantum group base
d on its Hopf-algebra structure and characters of the compact quantum grou
p. Then we will show the dynamics preserve the center of the group von Neu
mann algebra\, and it gives the dynamics on the unitary dual. Moreover\, t
he dynamics have generators\, and we can describe it explicitly by the rep
resentation theory. In particular\, we will deal with the case of quantum
unitary groups.\n\nPlease contact uwe.franz@univ-fcomte.fr for the link (i
t is same link as the previous seminar).\n
LOCATION:https://researchseminars.org/talk/AnalyseFonctionnelle/6/
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