Friday, **October 220**, 10:00 - 11:00, Jeff 222 and via Zoom

Michael Brannan (Waterloo)

On the von Neumann algebras of quantum automorphism groups of finite dimensional C*-algebras.

I will report on some ongoing work with Floris Elzinga (Oslo), Samuel Harris (TAMU), and Makoto Yamashita (Oslo), where we study the II_1-factors that arise as the quantum automorphism groups of finite-dimensional C*-algebras. Among other things, we show that many of these von Neumann algebras are strongly 1-bounded (in particular, they are not isomorphic to free group factors), and that they are always Connes embeddable.

Friday, **October 15**, 10:00 - 11:00, via Zoom

Serban Belinschi (Toulouse)

Brown measure of polynomials in star-free variables, Part II

This talk will outline a method of finding/studying the Brown measure of an arbitrary polynomial in free, possibly non-selfadjoint random variables belonging to a tracial W^*-noncommutative probability space. After a brief reminder of the hermitization procedure and of what the Brown measure is, we shall look at how the linearization procedure applies to non-selfadjoint variables and how the Brown measure is found from the linearization matrix. We conclude by examining the (simplest) case, namely that of the sum of two free random variables. The talk is mostly based on the 2018 paper Serban T. Belinschi, Piotr Śniady, and Roland Speicher, Eigenvalues of non-Hermitian random matrices and Brown measure of non-normal operators: Hermitian reduction and linearization method..

Friday, **October 8**, 10:00 - 11:00, via Zoom

Serban Belinschi (Toulouse)

Brown measure of polynomials in star-free variables, Part I

This talk will outline a method of finding/studying the
Brown measure of an arbitrary \ polynomial in free, possibly
non-selfadjoint random variables belonging to a tracial
W^*-\ noncommutative probability space. After a brief
reminder of the hermitization procedure a\ nd of what the
Brown measure is, we shall look at how the linearization
procedure applies\ to non-selfadjoint variables and how the
Brown measure is found from the linearization m\ atrix. We
conclude by examining the (simplest) case, namely that of
the sum of two free r\ andom variables. The talk is mostly
based on the 2018 paper Serban T. Belinschi, Piotr Śn\ iady,
and Roland Speicher, Eigenvalues of non-Hermitian random
matrices and Brown measure\ of non-normal operators:
Hermitian reduction and linearization method..

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