Functional Analysis Seminar  

  We meet in Blocker 302,  11:10am-12:10pm  Wednesdays for the Fall 2026 semmester. 

Schedule Fall 2026

• Sept. 2nd, Guihua Gong (University of Puerto Rico)

Title: Invariant and classification of simple amenable Z-stable C*-algebras and homomorphisms

Abstract: In this lecture, I will present the classification theorem of simple projectionless C*-algebras. This is a joint work with Huaxin Lin.

• Sept. 9, Haonan Zhang (South Carolina)

Title: On the König Constant

Abstract: König’s bilinear form arose in the study of the Grothendieck constant. König conjectured its optimal value in every dimension; had the conjecture been true, it would have determined the Grothendieck constant. A celebrated result of Braverman, K. Makarychev, Y. Makarychev, and Naor showed that the conjecture already fails in dimension two. In this talk, I will present examples, discovered with ChatGPT serving as a research assistant, that determine the König constant in the high-dimensional limit. This is joint work with Xinyuan Xie (UC Irvine).

• Sept. 16. No seminar

• Sept. 23,  Ajay Kumar Karri (TAMU)

Title: Decomposability and Norm Convergence property of Operators in Type I_k von Neumann Algebras

Abstract: 

We investigate the norm convergence of the sequence $\left\{\lvert A^n\rvert^{1/n}\right\}_{n\in\mathbb{N}}$ for operators $A$ in type $I_k$ (k is finite) von Neumann algebras acting on a separable Hilbert spaces. We prove that every such operator is decomposable and, consequently, that its normalized power sequence converges in norm. The argument uses continuous upper-triangular representations and suitable projection-valued families. As a consequence, our result recovers and extends several previously known norm convergence property for matrices, compact operators acting on a separable Hilbert space, Spectral operators, and Riesz operators. Finally, we exhibit an example in the type $I_\infty$ factor $\mathcal{B}(\ell^2(\mathbb{N}))$ for which norm convergence property fails, demonstrating the essential role of the finite parameter $k$.

• Sept. 30, Yoonkyeong Lee (TAMU)

Title : strong convergence to operator valued semicirculars

Abstract: Strong convergence requires convergence of operator norms of all polynomial expressions.  In this talk, we will discuss convergence of moments and strong convergence, how covariance maps describe the limiting behavior of general Gaussian random matrices. Then I will present a strong convergence theorem for operator valued semicircular models and illustrate the matrix models for the interpolated free group factor, using an integral covariance map on L^\infty[0,1]. This is joint work with David Jekel, Brent Nelson, and Jennifer Pi.

• Oct. 7, Brent Nelson (Michigan State)

Title: L2-functional calculus and the invariance of 1-bounded entropy

Abstract: The L2-functional calculus is a framework developed by David Jekel for expressing arbitrary elements of a tracial von Neumann algebra in terms of a fixed generating tuple. This expression is L2-Lipschitz in the sense that if the original tuple is replaced by another that is close in L2-norm, then the resulting outputs will likewise be close in L2-norm. Moreover, this Lipschitz constant is universal in the sense that the same inequality holds in all tracial von Neumann algebras. Consequently, this functional calculus is quite useful in free probability theory. In this talk, I will elaborate on these ideas and show how they provide a straightforward proof of the von Neumann algebraic invariance of 1-bounded entropy.

• Oct. 14th  Chris Gartland (North Carolina)

Title: Hyperbolic Group Actions on lp

Abstract: A finitely generated group is said to have the Haagerup property if it admits an isometric representation on l2 with a proper cocycle. Groups with Property (T), including some hyperbolic groups, cannot satisfy the Haagerup property. Shalom's conjecture asks whether every hyperbolic group satisfies a weaker version, namely: does every hyperbolic group admit a uniformly bounded representation on l2 with a proper cocycle? In this talk, we will explain how to use hyperbolic fillings to obtain the following result: every hyperbolic group G admits a uniformly bounded representation on lp with a proper cocycle, where p < Q/(Q-1) and Q is the conformal dimension of the boundary of G. Based on joint work with Tianyi Zheng.

• Oct. 28, David Larson (TAMU)

• Nov. 4, Pradyut Karmakar (Sam Houston State)

• Nov. 11, 

Schedule Spring 2026

• Apr. 20th    Zhiyuan Yang (TAMU)

Title: Relative biexact von Neumann algebras and amalgamated free product

Abstract: The study of biexact groups was initiated by Ozawa in his study of solidity of group von Neumann algebras. This notion was recently generalized to von Neumann algebras by Ding and Peterson. We will discuss some properties of relative biexact von Neumann algebras. And we will also show that the amalgamated free product of two weakly exact tracial von Neumann algebras over an amenable subalgebra is relative biexact. This is joint work with Kai Toyosawa.

• Apr. 15th     Eric Ricard (U. de Caen)

Title: "Riesz-Schur transform"

Abstract: We introduce a kind of Riesz transforms on Schatten classes. They turn out to be efficient tools to get results on Schur multipliers.

As an illustration, we will explain how to recover the Hormander-Mikhlin theorem on Fourier multipliers on Lp with an almost Hilbertian proof.

This is a joint work with Adrián González-Pérez, Javier Parcet and Jorge Pérez Garcı́a.

• Apr. 13th      Yoon Keyong Lee(Michigan State )

Title : On the genericity of Irreducible subfactors 

Abstract : (Joint work with Brent Nelson) In this talk we investigate the anticoarse space of the von Neumann algebras generated by the kernel and the domain of a closable derivation. We show that when a tuple (x_i)_{i\in I} admits a conjugate system, then for any proper subset J \subset I  with |J| \geq 2 the inclusion W*(x_j :j \in J) \subset W*(x_i: i \in I) is irreducible, infinite index and non- regular.  

• Mar. 16th   Ping Zhong (U. of Houston)

Title: On the Brown measure of X+iY with Y free Poisson

Abstract: Let X, Y be freely independent self-adjoint random variables with Y having Marchenko–Pastur distribution. We develop a method for computing the Brown measure of X+iY. Our approach relies on the matrix-valued subordination function Ω of the Hermitization of X+iY, together with the fact that Ω has an explicitly described left inverse H. This approach extends some methods developed in earlier works on additions with circular or semicircular elements.

The Brown measure becomes more tractable when it is reparametrized through a change of variables induced by the boundary values of the function H. The resulting formula for the Brown measure is expressed in terms of this new parameterization. Moreover, the Brown measure appears to coincide with the limiting eigenvalue distribution of the corresponding random matrix model.

This is joint work with Franz Lehner, Alexandru Nica, and Kamil Szpojankowski.

• Mar. 2nd       Jose Carrion   (TCU)

Title: $K_1$-injectivity and $KK$-uniqueness

Abstract: A unital C$^*$-algebra is $K_1$-injective if every unitary with trivial $K_1$-class is homotopic to the identity without the need for matrix amplifications. A long-standing open question asks whether all properly infinite C$^*$-algebras are $K_1$-injective. Through Paschke duality, this question is closely tied to a fundamental uniqueness problem in $KK$-theory.

I will describe joint work with Gabe, Schafhauser, Tikuisis, and White giving an affirmative answer after tensoring with the Jiang-Su algebra $\mathcal{Z}$, and how this was used in classification theory of nuclear C$^*$-algebras. I will then discuss recent work of Szabó, who proved $KK$-uniqueness in full generality.

• Feb. 23rd     Carl Pearcy   (TAMU)

Title: On a generalization of a theorem of Lomonosov

Abstract. Fifty three years ago Victor Lomonosov proved the remarkable theorem that every nonzero compact operator acting on a complex Banach space has a nontrivial hyperinvariant subspace (n.h.s.) and, more generally, that every nonscalar operator that commutes with such a compact operator has a n. h. s. But since then, no real improvement of the first above theorem has been made, even in the context of Hilbert space. 

For several years the speaker

has been trying to prove a beautiful generalization of the first theorem above, namely that every 2 x 2 operator matrix of the form

K.   C

0.   B

acting on the direct sum of an infinite dimensional complex Hilbert space with itself, where K is a nonzero compact operator, has a n. h.s.

 The speaker in his talk will discuss several partial solutions of this problem that he has made in the last few years.

• Feb. 16 Ajay Kumar Karri (Texas A&M)

Title: RESULTS ON GENERAL TOEPLITZ RANDOM MATRICES

Abstract: We prove the convergence of $*$-moments of Toeplitz matrices in two cases: (1) matrix entries are independent Gaussian random variables and (2) matrix entries are free semicircular entries. We also study joint $*$- moments of Toeplitz matrices in both cases with $ L^\infty[0,1]$ functions.

Schedule 2025

• Nov. 14.      Victor Bailey( U. Oklahoma)  

• Oct. 31.       Junchen Zhao (Texas A&M)

• Oct. 17       David Blecher (U of Houston)

•  Sept. 26. Akihiro Miyagawa (UC San Diego)

• Sep. 19 Merdad Kalantar (Oxford)

•