Functional Analysis Seminar  

  We meet in Blocker 302,  11am-noon Mondays. 

Schedule 2026

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

• 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. 27th    Zhiyuan Yang

• 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.

• 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.

• 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.

• 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.

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)

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