Analysis   Seminar    


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

September 11                Janusz Wysoczański,  University of Wroclaw
                                       Finitely Generated Weakly Monotone C*-algebras

                              

                               Abstract: In this talk I will present construction and properties of C*-algebras generated by finite number of creation/annihilation operators,  

                               acting on (weakly monotone) subspace of the full Fock space, related to Pusz-Woronowicz Twisted Canonical Commutation Relations. They

                                        happen to be quotients of Cuntz-Krieger algebras and are related to Hong-Szymanski's C*-algebras of quantum odd dimensional spheres. Graph
                                        algebra's point of view will be presented. Maximal abelian sub-algebra and its spectrum will be considered and identified.


September 18                Wenbo Sun,  Virginia Tech
                                       Geometry Ramsey Conjecture over finite fields

                                       Abstract: The Geometry Ramsey Conjecture is a question raised by Graham in 1994, which says that given any finite configuration X which lies on a
                                       sphere, for any finite coloring of the Euclidean space, there always exists a monochromatic congruent copy of tX for any large enough scalar t. One
                                       can also formulate a similar question for the finite field setting. While the study of the Geometry Ramsey Conjecture in literature focuses on the
                                       harmonic analysis approach, in this talk, we will explain how the higher order Fourier analysis method can be used to answer the Geometry Ramsey
                                       Conjecture in the finite field setting.


September 25                Jakob Streipel,  SUNY at Buffalo
                                       Stechkin's trick

                                       Abstract: In this talk we'll discuss a somewhat forgotten inequality from the 1970's due to S. B. Stechkin, and how it can be used to improve
                                       zero-free regions of L-functions by combining it with the standard approach due to de la Vallée Poussin in 1896. As we will demonstrate, this
                                       simple inequality lets one improve any zero-free region argument that uses a so-called explicit formula, and as an example we will talk about
                                       recent and ongoing joint work with Steven Creech, Alia Hamieh, Simran Khunger, Kaneenika Sinha, and Kin Ming Tsang where we use this trick
                                       (and other tools) to find an explicit zero-free region for L-functions of modular forms.            
 

October 16                    Jingbo Xia,  SUNY at Buffalo
                                      The Helton-Howe trace formula for the Drury-Arveson space

                                      Abstract: The famous Helton-Howe trace formula was originally established for antisymmetric sums of Toeplitz operators on the Bergman space
                                      of the unit ball. We prove its analogue on the Drury-Arveson space.


October 23                    Raphael Ponge,   Sichuan University
                                      Noncommutative Geometry, Semiclassical Analysis, and Weak Schatten Classes

                                      Abstract: In this talk, I will present new results regarding semiclassical Weyl's laws in the setup of Connes' noncommutative geometry. They provide
                                      precise asymptotics for the counting functions of Schroedinger operators under the semiclassical limit. This improves and simplifies previous
                                      results of McDonald-Sukochev-Zanin. This provides a bridge between semiclassical analysis and noncommutative geometry. Thanks to the Birman-
                                      Schwinger principle and old results of Birman-Solomyak this reduces to establishing various weak Schatten class properties for operators at stake.
                                      This has a number of applications. We shall present two of them. First, we recover previously known semiclassical Weyl's laws on Euclidean domains
                                      and closed manifolds. These results were proved in 60s and 70s. However, thanks to our setup, they can be deduced results of Minakshisundaram
                                      and Pleijel on short time heat kernel asymptotics for Laplacians that were established in the late 40s. Second, we obtain semiclassical Weyl laws for
                                      noncommuative tori for any dimension. These laws were conjectured by Ed McDonald and the speaker.


November 13                Joseph Leung,   Rutgers University         
                                      Second moment for GL(3) L-functions in the critical line

                                      Abstract: We discuss the second moment for the GL(3) standard L-functions on the critical line. When the GL(3) form is specialized as the Eisenstein
                                      series, this is the infamous sixth moment of the zeta function. In a joint work with Matthew Young and Agniva Dasgupta, we obtain a nontrivial
                                      upper bound for this moment. This work is inspired by the short second moment result achieved by Aggarwal, Leung, and Munshi. We will discuss
                                      the key ideas of the proof and its applications, which include an improvement on the Rankin-Selberg problem.                                      
                                    

 
Past Analysis Seminar