Unless specified, all seminars are Wednesday 4-5pm at 250 Math Building.

January 13th Organizational Meeting

January 27th Hanfeng Li, SUNY at Buffalo

Entropy and Fuglede-Kadison determinant, Part I

Abstract: For any discrete group G and any element f in the integral group ring ZG of G, one may consider the algebraic action of G associated to f, i.e., the shift action of

G on the Pontryagin dual of ZG/ZGf. When G is amenable, the entropy is defined for actions of G. I will discuss the relation between the entropy of the above algebraic

action and the Fugelde-Kadison determinant of f in the group von Neumann algebra of G.

February 3rd Hanfeng Li, SUNY at Buffalo

Entropy and Fuglede-Kadison determinant, Part II

February 11th David Kerr, Texas A&M University

(Thursday, Colloquium) Topological entropy for actions of sofic groups

Abstract: Recently Lewis Bowen introduced a notion of entropy for measure-preserving actions of sofic groups which he used to solve the Bernoulli shift isomorphism

problem for a large class of nonamenable groups. I will show that by taking an operator-algebraic viewpoint one can define a topological version of Bowen's measure

entropy and then discuss how the two are related via a variational principle.

February 24th

Heat flow, BMO, and the compactness of Toeplitz operators

Abstract: Given a BMO

Segal-Bargmann space H

all t > 0. Moreover, we discuss the same question in the context of the weighted Bergman space of the unit ball, discuss what implications these results have for the

compactness of Toeplitz operators in both the weighted Bergman and Segal-Bargmann space situation, and finally discuss some new compactness and Schatten class

membership results for Toeplitz operators on H

March 17th Jonathan Dimock, SUNY at Buffalo

Renormalization Group Methods

March 31st Nikolai Vasilevski, CINVESTAV del I.P.N., Mexico

On compactness of commutators and semi-commutators of Toeplitz operators on the Bergman space

April 7th David Blecher, University of Houston

One-sided ideals and structure of operator algebras

Abstract: We begin by describing a new noncommutative topology for (possibly nonselfadjoint) operator algebras, related to the concept of `open projections' for

C*-algebras. We connect some of this to some ideas in Banach algebra theory, and use it to study the structure of a new class of nonselfadjoint algebras.

April 15th Dechao Zheng, Vanderbilt University

(Thursday, Colloquium) The spectrum and essential spectrum of Toeplitz operators with harmonic symbols

Abstract: On the Hardy space, by means of an elegant and
ingenious argument, Widom showed that the spectrum of a bounded
Toeplitz operator is always connected

and Douglas showed that the essential spectrum of a bounded Toeplitz operator is also connected. On the Bergman space, McDonald and Sundberg showed that the

essential spectrum of T_{φ}
is connected for φ a harmonic function on D if φ is
either real-valued or piecewise continuous on the boundary of the unit
disk. They asked

the problem whether the essential spectrum of a Toeplitz operator on the Bergman space with bounded harmonic symbol is connected. In my talk, I will present my joint

work with Sundberg to show examples that the spectrum and the essential spectrum of a Toeplitz operator with bounded harmonic symbol is disconnected.

and Douglas showed that the essential spectrum of a bounded Toeplitz operator is also connected. On the Bergman space, McDonald and Sundberg showed that the

essential spectrum of T

the problem whether the essential spectrum of a Toeplitz operator on the Bergman space with bounded harmonic symbol is connected. In my talk, I will present my joint

work with Sundberg to show examples that the spectrum and the essential spectrum of a Toeplitz operator with bounded harmonic symbol is disconnected.

Past Analysis Seminars