# Colloquium: Tuesday, October 23, 2018. Speaker: Ami Viselter (University of Haifa). Title: “Convolution semigroups on quantum groups and non-commutative Dirichlet forms”.

Department of Mathematics                                                           University of  Haifa

Colloquium

Speaker: Ami Viselter (University of Haifa)

Topic: Convolution semigroups on quantum groups and non-commutative Dirichlet forms

Place: Room 614 in the Science & Education Building

Time: 14:00

Date: Tuesday, October 23, 2018

Abstract:

We will discuss convolution semigroups of states on locally compact quantum groups. They generalize the families of distributions
of L\’evy processes from probability. We are particularly interested in semigroups that are symmetric in a suitable sense. These are proved to be in one-to-one correspondence with KMS-symmetric Markov semigroups on the $L^\infty$ algebra that satisfy a natural commutation condition, as well as with non-commutative Dirichlet forms on the $L^2$ space that satisfy a natural translation invariance condition. This Dirichlet forms machinery turns out to be a powerful tool for analyzing convolution semigroups as well as proving their existence. We will use it to derive geometric characterizations of the Haagerup Property and of Property
(T) for locally compact quantum groups, unifying and extending earlier partial results. Based on joint work with Adam Skalski.

Tea will be served before the talk.

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