BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT 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/ END:VEVENT 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/ END:VEVENT END:VCALENDAR