## Les événements de septembre 2020

• ### Lundi 21 septembre 11:00-12:00 - Jean-Jil Duchamps - LmB, Univ. Bourgogne Franche-Comté

Séminaire PS : La forêt de Moran

Résumé : On considère la forêt aléatoire obtenue sous la distribution stationnaire de la chaîne de Markov suivante sur les graphes sur 1, ..., n : à chaque étape, un sommet choisi uniformément est déconnecté de ses voisins et reconnecté à un autre sommet choisi uniformément. Cette forêt aléatoire correspond aux liens de parenté direct entre individus dans une population évoluant selon un modèle classique (modèle de
Moran). Elle admet une construction très simple que j’expliciterai, qui permet de révéler les liens intéressants qu’elle présente avec l’arbre uniforme sur 1, ... , n, ainsi qu’avec les "uniform attachment trees". Je donnerai aussi certaines de ses caractéristiques : loi des degrés, d’un arbre uniforme, taille du plus grand degré/arbre (travail en collaboration avec F. Bienvenu et F. Foutel-Rodier).

Lieu : Salle 316B - LmB

• ### Mardi 8 septembre 13:45-15:00 - Jacek Krajczok - IMPAN, Warsaw

Type I locally compact quantum groups : coamenability and applications

Résumé : We say that a locally compact quantum group is type I if its
universal C* algebra (which is equal to $C^u_0(\hatG)$) 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 13:45-15:00 - Biswarup Das - Wroclaw University

Towards quantizing separate continuity : A quantum version of Ellis joint continuity theorem

Résumé : 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.

• ### Mercredi 16 septembre 14:00-17:00 -

Séminaire de rentrée de l’IREM

Lieu : LmB, salle 316Bbis

• ### Mardi 15 septembre 16:30-18:00 -

Réunion de rentrée du LmB

Lieu : Amphi A (UFR ST)