Analysis   Seminar    

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

January 13th                               Organizational Meeting    
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  

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                            
Joshua Isralowitz,    SUNY at Buffalo
                                                  Heat flow, BMO, and  the compactness of Toeplitz operators

                                                  Abstract: Given a  BMO1  function f on Cn, we can take the Berezin transform (better known as the ``heat transform") f~(t0) of f  with respect to the weighted
                                                  Segal-Bargmann space  H2 (Cn, dμt0). In this talk, we discuss the question of whether f~(t0)  vanishing at infinity for some t0 > 0 implies that f~(t) vanishes at infinity for
                                                  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 H2 (Cn, dμt).  This is joint work with W. Bauer and L. Coburn.

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 Tφ 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.

Past Analysis Seminars