Analysis   Seminar    

Unless specified, all seminars are Wednesday 4-5pm via Zoom, or both Room 250 and Zoom.  For Zoom information please send email to                                                             

August 31                     Yi Wang,   Chongqing University                                                    
8PM, Zoom                 
Helton-Howe trace, Connes-Chern character and quantization

                                      Abstract: We study the Helton-Howe trace and the Connes-Chern character for Toeplitz operators on weighted Bergman spaces via the idea of
                                      quantization. We prove a local formula for the large t-limit of the Connes-Chern character as the weight goes to infinity. And we show that the
                                      Helton-Howe trace of Toeplitz operators is independent of the weight and obtain a local formula for the Helton-Howe trace for all weighted Bergman
                                      spaces. The proofs
are based on an integration by parts formula and some harmonic analysis. This talk is based on joint work with Xiang Tang and
                                      Dechao Zheng.

September 7                  Mariusz Tobolski,   University of Wroclaw                                            
The Stone-von Neumann theorem for locally compact quantum groups

                                      Abstract: The Stone-von Neumann theorem is a mathematical result that rigorously proves the equivalence between the two fundamental approaches
                                      to quantum mechanics, i.e. the matrix mechanics of Heisenberg and the wave mechanics of
Schrödinger. It was then formulated by Mackey as a
                                      theorem about certain unitary representations of locally compact abelian groups. In my talk, based on yet another formulation due to Rieffel, I will
                                      present a Stone-von Neumann-type theorem in the setting of locally compact quantum groups introduced by Kustermans and Vaes and
                                      independently by Woronowicz.

September 14                Hanfeng Li,   SUNY at Buffalo                                      
250 and Zoom             
Entropy and asymptotic paris

                                      Abstract: Positive entropy and the existence of nontrivial asymptotic pairs are both kind of chaotic properties in topological dynamics. I will discuss
                                      the relation between these two properties for algebraic actions of amemable groups, and how this is related to the strong Atiyah conjecture in
                                      L2-invariants theory. This is joint work with Sebastian Barbieri and Felipe Garcia-Ramos. 

October 12                     Yuqing (Frank) Lin,   Texas A&M University                                      
250 and Zoom             
Entropy for actions of free groups under bounded orbit equivalence

Joint work with Lewis Bowen.  The f-invariant is a notion of entropy for probability measure preserving (pmp) actions of free groups.  It is
                                       invariant under measure conjugacy and is an extension of Kolmogorov-Sinal entropy for actions of the integers.  Two pmp actions are orbit
                                       equivalent if their orbits can be matched almost everywhere in a measurable fashion.  Although entropy is not invariant under orbit equivalence in
                                       general, work of Austin and Kerr-Li has shown in various settings that entropy is invariant under certain stronger notions of quantitative orbit
                                       equivalence.  We add to these results by showing that the f-invariant is invariant under the assumption of bounded orbit equivalence.

November 9                   Hongming Nie,   SUNY at Stony Brook                                    
250 and Zoom
               A metric on hyperbolic components

                                       Abstract: In this talk, under a mild condition, I will introduce a metric on hyperbolic components of rational maps. This metric is constructed by
                                       considering the measure-theoretic entropy with respect to some equillibrium state. Moreover, this metric is conformal equivalent to the pressure
                                       metric from the thermodynamics. It is a joint work with Y.M. He.

November 16                 Sagun Chanillo,   Rutgers University                                      
Local Version of Courant's Nodal Domain Theorem

Abstract: Let $(M^n ,g)$ denote a smooth, compact Riemannian manifold with no boundary. A fundamental object on this manifold is the
                                       Laplace-Beltrami operator which has a discrete spectrum. If we arrange the eigenvalues of the Laplacian in increasing order (for the negative of the
                                       Laplacian) with multiplicity, Courant's theorem states, that the number of nodal components for the k-th eigenfunction is at most k. A nodal
                                       component of an eigenfunction u is the connected component of the set where u does not vanish. In this talk we study a local version of this
                                       global result of Courant. The local question was raised by Donnelley and C. Fefferman in the late 1980s. Our theorems are joint work with
                                       A. Logunov, E. Mallinikova and D. Mangoubi.

November 30                  Joseph Hundley,   SUNY at Buffalo   
Functorial Descent in the Exceptional Groups

                                       Abstract: In this tallk, I will discuss the method of functorial descent. This method, which was discovered by Ginzburg, Rallis and Soudry, uses Fourier
                                       coefficients of residues of Eisenstein series to attack the problem of characterizing the image of Langlands functorial liftings. We'll discuss the
                                       general structure, the results of Ginzburg, Rallis and Soudry in the classical groups, some recent attempts to extend the same ideas to the
                                       exceptional groups, and challenges and new phenomena which emerge in these attempts. The new work discussed will mainly be joint with Baiying
                                       Liu. Time permitting I may also comment on unpublished work of Ginzburg and joint work with Ginzburg.

Past Analysis Seminar