## Séminaire d’Analyse Fonctionnelle

publié le , mis à jour le

Le séminaire a lieu le mardi à 13h45, en salle 316Bbis du bâtiment de
Métrologie (plan d’accès). Pour le moment, les expos és sont virtuels (pour le lien, contactez la responsable).

Vous trouverez ci-dessous le planning du séminaire d’Analyse
Fonctionnelle pour l’année universitaire en cours.
L’historique des séminaires des années précédentes se trouve
ici.

Pour contacter la responsable (Yulia Kuznetsova) : yulia.kuznetsova@univ-fcomte.fr.
Pour s’abonner au séminaire : ACM.

### Exposés à venir

-Mardi 6 octobre, 13:45: Jean-Christophe Bourin, LMB
Une décomposition pour les matrices partitionnées

On établit "un théorème de Pythagore" pour les matrices partitionnées qui entraîne de nombreuses inégalités.

-Mardi 20 octobre, 13:45 (en ligne): Jonas Wahl, Hausdorff Center for Mathematics, Bonn
Markov dynamics on branching graphs of diagram algebras

Thoma's famous theorem on the classification of characters on the infinite symmetric group has been very influential in different areas of mathematics such as combinatorics and probability theory. In this talk, we explain versions of Thoma's theorem for different diagram algebras arising out of subfactor theory and Banica and Speicher's theory of easy quantum groups. As Thoma's classical theorem, these results can be formulated in a probabilistic language and we find interesting new connections to random lattice paths and random walks on trees.

## Septembre

-Mardi 8 septembre, 13:30 (en ligne): Jacek Krajczok, IMPAN, Warsaw
Type I locally compact quantum groups: coamenability and applications

We 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 quantum 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 representations. I will discuss a result which states that coamenability of G is 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 compact quantum groups to show that the quantum space underlying the Toeplitz algebra does not admit a quantum group structure (joint work with Piotr Sołtan).

-Mardi 22 septembre, 13:45 (en ligne): Biswarup Das, Wroclaw University
Towards quantizing separate continuity: A quantum version of Ellis joint continuity theorem

Let S be a topological space, which is also a semigroup with identity, such that the multiplication is separately continuous. Such semigroups are called semitopological 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 algebraically speaking, S is a group (i.e. every element has an inverse). (c) The multiplication is separately continuous as above (no other assumption. This is the only assumption concerning the interaction of the topology with the group structure). Then it follows that S becomes a topological 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 continuity theorem. In this talk, we will prove a non-commutative version of this result. Upon briefly reviewing the notion of semitopological semigroup, we will introduce ''compact semitopological quantum semigroup'' which were before introduced by M. Daws in 2014 as a tool to study almost periodicity of Hopf von Neumann algebras. Then we will give a necessary and sufficient condition 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 theorem as well. This is the joint work with Colin Mrozinski.

-Mardi 29 septembre, 13:45, salle 316B: Uwe Franz, LMB
Quelques applications de la cohomologie de Hochschild aux probabilités non commutatives

Les semi-groupes de convolution d’états sur un espace de probabilités non commutatif sont en général caractérisés par leur dérivée en t=0, qu'en appelle leur fonctionnelle génératrice. Une telle fonctionnelle $\psi$ peut être complétée en un triplet $(\rho,\eta,\psi)$, dont les composantes sont caractérisées par des relations cohomologiques. Dans mon expose je vais rappeler la cohomologie de Hochschild ainsi que cette construction. Ensuite nous allons regarder quelques applications du premier et deuxième groupes de cohomologie à l’étude des fonctionnelles génératrices.

## Agenda

• ### Mercredi 19 mai 2021 13:45-15:00 - Victor Nistor - Metz

Séminaire d’Analyse Fonctionnelle