Oberseminar Free Probability

In this research seminar we treat topics ranging from free probability and random matrix theory to combinatorics, operator algebras, functional analysis and quantum groups.

Talks

Mi, 4.11., 16:15 - Daniel Gromada (Saarbrücken), Group-theoretical graph categories

In the talk, we are going to recall the definition of group-theoretical categories of partitions [Raum–Weber '14] and skew categories of
partitions [Maaßen '18]. We will then generalize those structures into the framework of graph categories (in the sense of Mančinska–Roberson) and introduce some kind of group-theoretical description also here.  We also discuss the quantum groups associated to such categories. The talk is based on a recent preprint arXiv:2009.06998.


Mi, 11.11., 16:15 - Hannes Thiel (Münster/Dresden), Diffuse traces and Haar unitaries

A Haar unitary (with respect to a given tracial state) is a unitary such that every nonzero power of the unitary and its adjoint has vanishing trace. We show that a tracial state admits a Haar unitary if and only if it is diffuse (the unique extension to a normal tracial state on the enveloping von Neumann algebra vanishes on every minimal projection), if and only if it does not dominate a tracial functional that factors through a finite-dimensional quotient.

It follows that a unital C*-algebra has no finite-dimensional representations if and only if each of its tracial states admits a Haar unitary. In particular, every tracial state on an infinite-dimensional, simple C*-algebra admits a Haar unitary.

I will sketch a proof of this result and present some applications to group C*-algebras and reduced free products.


Mi, 18.11. + Mi, 25.11. + Mi, 2.12., 14:00 (sharp) - Loop models meet diagram algebras

(A series of talks, details to be announced)


Mi, 9.12. - Nicolas Faroß (Saarbrücken), Towards a Concrete Model for the Quantum Permutation Group