Analysis   Seminar    

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

September 29                Jingbo Xia,   SUNY at Buffalo                                                    
The Helton-Howe trace formula for submodules


October  20                   Xin Ma,   University of Memphis
Fiberwise amenability and almost elementariness for \'{e}tale groupoids      

In this talk, I will discuss two new properties for locally compact Hausdorff \'{e}tale groupoids. One is from a coarse geometric view
                                      called fiberwise amenability. Another one is called almost elementariness, which is a new finite-dimensional approximation property. I will explain
                                      how these notions relate to almost finiteness defined by Matui and refined by Kerr and show our almost elementariness implying tracial Z-stability
                                      of reduced groupoid C*-algebras. As an application. This implies that Matui's almost finiteness in the groupoid setting also implies Z-stability when
                                      the groupoid is minimal 2nd countable and topological amenable. This was open in general before. I will also present more applications if time
                                      permits. This is based on joint work with Jianchao Wu.           

November 3                 
Nathan Wagner,  Washington University in St.Louis
                                      Weighted sstimates for the Bergman and Szego projections on strongly pseudoconvex domains 

                                      Abstract: The Bergman and Szego projections are fundamental operators in complex analysis in one and several complex variables. Consequently,
                                      the mapping properties of these operators on L^p and other function spaces have been extensively studied. In this talk, we discuss some recent
                                      results for these operators on strongly pseudoconvex domains with near minimal boundary smoothness. In particular, weighted L^p estimates are
                                      obtained, where the weight belongs to a suitable generalization of the Bekolle-Bonami or Muckenhoupt class. For these domains with less
                                      boundary regularity, we use an operator-theoretic technique that goes back to Kerzman and Stein. We also obtain weighted estimates for the
                                      endpoint p=1, including weighted weak-type (1,1) estimates. Here we use a modified version of singular-integral theory and a generalization of the
                                      Riesz-Kolmogorov characterization of precompact subsets of Lebesgue spaces. This talk is based on joint work with Brett Wick and Cody Stockdale.

November 10                Sherry Gong,  Texas A&M University
Non-orientable link cobordisms and torsion order in Floer homologies

In a recent paper, Juhasz, Miller and Zemke proved an inequality involving the number of local maxima and the genus appearing in an
                                      oriented knot cobordism using a version of knot Floer homology. In this talk I will be discussing some similar inequalities for non-orientable knot
                                      cobordisms using the torsion orders of unoriented versions of knot Floer homology and instanton Floer homology. This is a joint work with Marco

November 17                Byung-Jay Kahng,   Canisius College
Construction of a C*-algebraic quantum groupoid from purely algebraic data

To properly develop a theory of C*-algebraic quantum groupoids, some rather technical notions such as relative tensor product of Hilbert
                                      spaces are needed, which can be daunting. Things can become simpler if there exists a certain projection, E, which can be considered as Delta(1). At
                                      the purely algebraic level, there exists a natural notion called Weak Multiplier Hopf algebras, which include as special cases Hopf algebras, Multiplier
                                      Hopf algebras, and Weak Hopf algebras.                                       In this talk, we will start from only a purely algebraic data of a WMHA, assuming the existence of a left-invariant functional, and aim to construct a
                                      C*-algebraic object, which should be a C*-algebraic quantum groupoid.  The construction data will be all purely algebraic, and we will use tools from
                                      the (vN and C*-) weight theory.

December 1                   Alexandru Chirvasitu,  SUNY at Buffalo
                                       Chain groups and center reconstruction for locally compact groups

                                       Abstract: A result of Muger's says that the center of a compact group G can be recovered from the category of G-representations as the dual of the
                                       chain group of that category: the universal group by which the category in question can be graded.

                                       Trying to extend this to locally compact groups raises a number of interesting questions I will mention, along with extensions of Muger's theorem to
                                       various classes of groups (e.g. discrete groups with infinite conjugacy classes, semisimple connected Lie groups, and others).

December 8                   Jiseong Kim,   SUNY at Buffalo
Shifted sums of Hecke eigenvalue squares

Abstract: The additive divisor problem states some asymptotic formulas for shifted convolution sums of two divisor functions. This problem is still
                                       open, but Matomaki, Radziwill and Tao showed that the asymptotic formulas hold for almost all shifts. In this talk, we will talk about an analogue of
                                       the additive divisor problem for Hecke eigenvalue squares.

Past Analysis Seminar