
Date Time 
Location  Speaker 
Title – click for abstract 

01/27 4:00pm 
BLOC 306 
Ken Dykema TAMU 
On spectral and decomposable operators in finite von Neumann algebras.
We describe spectral and decomposable operators on Hilbert spaces and then, in the case of operators belonging to finite von Neumann algebras, relate these properties to the HaagerupSchultz subspaces of the operators. Finally, we will examine certain such operators arising naturally in free probability theory. 

02/03 4:00pm 
BLOC 306 
Ken Dykema TAMU 
On spectral and decomposable operators in finite von Neumann algebras. (cont.)
We describe spectral and decomposable operators on Hilbert spaces and then, in the case of operators belonging to finite von Neumann algebras, relate these properties to the HaagerupSchultz subspaces of the operators. Finally, we will examine certain such operators arising naturally in free probability theory. 

02/10 4:00pm 
BLOC 306 
Ken Dykema TAMU 
On spectral and decomposable operators in finite von Neumann algebras. (cont.)
We describe spectral and decomposable operators on Hilbert spaces and then, in the case of operators belonging to finite von Neumann algebras, relate these properties to the HaagerupSchultz subspaces of the operators. Finally, we will examine certain such operators arising naturally in free probability theory. 

02/17 4:00pm 
BLOC 306 
Michael Anshelevich TAMU 
Hermite trace polynomials
We consider the algebra of trace polynomials with the state induced by the GUE random matrices. In addition to the monomial basis, another natural basis for this algebra consists of the Hermite trace polynomials. They satisfy several properties familiar for the ordinary trace polynomials. The algebra structure can be extended from polynomials to a larger family of stochastic integrals. While the Hermite trace polynomials are not orthogonal, they can be modified to obtain several versions of the chaos decomposition. The simplest of these is related to the Hermite polynomials of matrix argument.
This is joint work with David Buzinski. 

02/27 09:00am 
ZOOM 
March Boedihardjo ETH Zurich 
Spectral norm and strong freeness
We give a nonasymptotic estimate for the spectral norm of a large class of random matrices that is sharp in many cases. We also obtain strong asymptotic freeness for certain sparse Gaussian matrices. Joint work with Afonso Bandeira and Ramon van Handel. References:  https://arxiv.org/abs/1504.05919
 https://arxiv.org/abs/2108.0631
 https://arxiv.org/abs/2208.11286
ZOOM LINK: https://tamu.zoom.us/j/97389162643 

03/03 4:00pm 
BLOC 306 
Ken Dykema TAMU 
On Bvalued circular operators
We will briefly introduce Bvalued circular operators, where B is a *algebra. We will describe (and perhaps prove) some results about these, in the special case when B is a commutative C*algebra and describe how they are relevant to the study of DToperators. 

03/06 09:00am 
ZOOM 
March Boedihardjo ETH Zurich 
Spectral norm and strong freeness: Proofs
I will begin by proving an estimate for a quantity introduced by Tropp. I will then give a combinatorial proof and an analytic proof of the main result in my previous talk. References:  https://arxiv.org/abs/2104.02662
 https://arxiv.org/abs/2108.06312
ZOOM LINK: https://tamu.zoom.us/j/97389162643 

03/24 4:00pm 
BLOC 306 
Zhiyuan Yang TAMU 
Modular structure of Hilbert space and twisted ArakiWoods algebras
We discuss the construction of Ttwisted ArakiWoods von Neumann algebras following the preprint https://arxiv.org/pdf/2212.02298.pdf by da Silva and Lechner, which is a generalization of the qArakiWoods algebras. We will begin with the basic properties of the modular operators of standard subspaces and its correspondence with the semigroup approach often used in qArakiWoods literature. Then we describe a sufficient and necessary condition (crossing symmetry and satisfying the YangBaxter equation) on the twist T for the vacuum vector to be separating. 

03/31 4:00pm 
BLOC 306 
Sheng Yin Baylor University 
Noncommutative rational functions in random matrices and operators.
It is wellknown that many random matrices have an asymptotical limit which is described by free probability. That is, for any noncommutative polynomial in these d independent random matrices converges to the same polynomial in d freely independent random variables that describe the limit distribution of each sequence of random matrices. In this talk, we will present a natural generalization of this convergence result. Namely, under suitable assumptions, we can enlarge our test function from noncommutative polynomial to noncommutative rational functions. It is based on a jointwork with Benoît Collins, Tobias Mai, Akihiro Miyagawa and Félix Parraud. 

04/14 4:00pm 
BLOC 306 
Michael Anshelevich TAMU 
TBA 

04/21 4:00pm 
BLOC 306 
Michael Anshelevich TAMU 
TBA 

04/28 4:00pm 
BLOC 306 
Michael Anshelevich TAMU 
TBA 