
Date Time 
Location  Speaker 
Title – click for abstract 

08/30 4:00pm 
BLOC 306 
Daniel Perales Texas A&M University 
Stransform in finite free probability
We show a simple way to obtain the limiting spectral distribution of a sequence of polynomials (with increasing degree) directly using their coefficients. Specifically, we relate the asymptotic behavior of the ratio of consecutive coefficients to Voiculescu's Stransform of the limiting measure. In the framework of finite free probability, this ratios of coefficients can be understood as a new notion of finite Stransform, which satisfies several analogous properties to those of the Stransform in free probability, including multiplicativity and monotonicity. We will mention some of the main ingredients of the proof that include topics of independent interest such as a partial order in the set of polynomials, and a simplified explanation of why free fractional convolution corresponds to the differentiation of polynomials. Then we will go over some applications. Joint work with Octavio Arizmendi, Katsunori Fujie and Yuki Ueda (arXiv:2408.09337). 

09/06 4:00pm 
BLOC 306 
Carl Pearcy Texas A&M University 
On restrictions of operators on Hilbert space to a half space 

09/20 4:00pm 
BLOC 306 
Ken Dykema Texas A&M University 
On operatorvalued Rdiagonal and Haar unitary elements (Joint work with John Griffin)
Rdiagonal elements are naturally defined by conditions on the free cumulants of the pair consisting of the element and its adjoint. In the tracial, scalarvalued context, it is known (due to pioneering work of Nica and Speicher) that being Rdiagonal is equivalent to having the same *distribution as an element with a polar decomposition z=uz, where u and z are *free and where u is a Haar unitary. In the operatorvalued context (namely, Bvalued where B is an operator algebra), this is no longer the case. Freeness need not occur, and even notions of Haar unitary are more complicated in the operatorvalued setting. We will (1) examine different notions of operatorvalued Haar unitary (2) introduce the notion of a free bipolar decomposition and (3) discuss a specific result about free bipolar decompositions of Bvalued circular elements (which are a very special case of Bvalued Rdiagonal elements) when B is twodimensional. 

10/11 4:00pm 
BLOC 306 
Carl Pearcy Texas A&M University 
A structure theorem for essentially quasinilpotent operators
In this talk it will be shown that every operator in a large class of essentially quasinilpotent operators, up to similarity, has a 3 x 3 operator matrix with particularly nice properties. 

10/18 4:00pm 
BLOC 306 
Tao Mei Baylor University 
Hilbert transform, Cotlar’s identity, and Hyperbolic groups
The classical Hilbert transform is a cornerstone of analysis, known for its fundamental role in both analysis and probability. A key approach to establishing its Lpboundedness is through Cotlar's identity, a powerful tool that not only yields optimal constants for the Lp bounds of the Hilbert transform but also generalizes to broader settings where the notion of "analytic functions" is meaningful. In this talk, I will revisit Cotlar’s identity and explore how modified versions extend to free groups and hyperbolic groups 

10/25 4:00pm 
BLOC 306 
Zhiyuan Yang Texas A&M University 
A dual of positive maps between von Neumann algebras with weights
We discuss a basic duality of positive maps between von Neumann algebras with faithful normal states introduced by L. Accardi and C. Cecchini in 1982. This duality was later generalized by Dénes Petz in 1984 to the cases of weights. We will prove this duality following Petz's argument. And as a direct application, we show that for any weight decreasing positive map (between von Neumann algebras with n.s.f. weight), there is a normal weight decreasing positive map such that these two positive maps coincide on the domain of the weight. In particular, this covers the wellknown fact that any state decreasing map is automatically normal. 

11/01 4:00pm 
BLOC 306 
Carl Pearcy Texas A&M University 
A structure theorem for a class of essentially quasinilpotent operators on Hilbert space
It is widely thought that quasinilpotent operators are the most difficult to understand. In this talk I will obtain a structure theorem for a class of such operators that may allow some progress in their understanding. 

11/08 4:00pm 
BLOC 306 
Carl Pearcy Texas A&M University 
On transitive subspaces of operators on finite dimensional Hilbert spaces
This topic has been around for awhile, but there are only a few papers that address it. I will discuss what I have learned about it and a few results that I have obtained. 

11/22 4:00pm 
BLOC 306 
Junchen Zhao Texas A&M University 
Free products and rescalings involving nonseparable von Neumann algebras
For a nonseparable selfsymmetric abelian von Neumann algebra A, we study rescalings of the free product of n copies of A with LF_r to define a new mutually nonisomorphic continuous family of nonseparable interpolated free products that has a rescaling formula and a free product addition formula. Explicit computations will be given to demonstrate welldefinedness of this family, their free product, and free products with finitedimensional or hyperfinite von Neumann algebras. Using this family, we can also show the Murrayvon Neumann fundamental group of the infinite free product of A is all of (0, \infty). This is joint work with Ken Dykema. 