Friday, December 3, 10:00 - 11:00, via Zoom
Nathan Pagliaroli (Western)
Introduction to Dirac ensembles
Finite spectral triples where the algebra is the space of $N \times N$ Hermitian matrices are examples of a matrix geometries. When matrix geometries are equipped with a probability measure we create an ensembles of Dirac operators. The Dirac operator’s finite size makes these ensembles of random matrices. Numerically evidence has recently shown that such models exhibit evidence of phase transitions as well as other interesting properties. In this talk we will discuss how to find these phase transitions in certain Dirac ensembles as well as how to compute their spectral density function.
Friday, November 19, 10:00 - 11:00, via Zoom
Mario Diaz (UNAM)
On the analytic structure of second-order non-commutative probability spaces
In this talk we present a general approach to the central limit theorem for the continuously differentiable linear statistics of random matrix ensembles. This approach, which is based on a weak large deviation principle for the operator norm, a Poincaré-type inequality for the linear statistics, and the existence of a second-order limit distribution, allows us to recover known central limit theorems and establish new ones. Furthermore, we define an analytic version of a second-order non-commutative probability space that allows us to recover in an abstract form some of the results obtained for the random matrix ensembles considered by our approach.
Friday, November 12, 10:00 - 11:00, via Zoom
Pei-Lun Tseng (NYU Abu Dhabi)
Infinitesimal Multiplicative Convolutions
In this talk, we first review notions of (operator-valued ) non-commutative infinitesimal independence and some basic properties. Then for each notion of infinitesimal independence, we introduce the corresponding infinitesimal transform and show such transform satisfy certain multiplicative property.
Friday, October 29, 10:00 - 11:00, via Zoom
Jamie Mingo (Queen's)
The Infinitesimal Weingarten Calculus.
I will give an interpretation of the subleading term of the Orthogonal Weingarten function in terms of non-crossing annular permutations.
Friday, October 22, 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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