| Date: | September 23, 2021 |
| Time: | 2:00pm |
| Location: | Zoom |
| Speaker: | Nathan Wagner, Washington University - St. Louis |
| Title: | Dominating Sets in Bergman Spaces on Strongly Pseudoconvex Domains |
| Abstract: | We obtain local estimates, also called propagation of smallness or Remez-type inequalities, for analytic functions in several variables. Using Carleman estimates, we obtain a three sphere-type inequality, where the outer two spheres can be any sets satisfying a boundary separation property, and the inner sphere can be any set of positive Lebesgue measure. We apply this local result to characterize the dominating sets for Bergman spaces on strongly pseudoconvex domains in terms of a density condition or a testing condition on the reproducing kernels. Our methods also yield a sufficient condition for arbitrary domains and lower-dimensional sets. This talk is based on joint work with Walton Green at Washington University in St. Louis. |
|
| Date: | September 30, 2021 |
| Time: | 2:00pm |
| Location: | BLOC 302 |
| Speaker: | Bernhard Lamel, Texas A&M University at Qatar |
| Title: | Finite determination of CR maps |
| Abstract: | We discuss some recent results about unique determination of CR maps. Starting from classical work of Cartan on finite determination of holomorphic maps from their 1-jet in the interior of domains, we discuss how boundary versions of these results give rise to the question of finite determination of CR maps, review some known results from the literature, and finally will try to outline the currently most comprehensive result for finite determination of CR maps in positive codimension. |
|
| Date: | October 28, 2021 |
| Time: | 2:00pm |
| Location: | BLOC 624 |
| Speaker: | John N. Treuer, Texas A&M University |
| Title: | Rigidity Theorems on planar domains |
| Abstract: | In this talk, using the analytic and logarithmic capacity we will investigate extremal properties of several kernel functions including the Bergman, Szego, higher-order Bergman kernels. We will then explore rigidity results concerning the logarithmic capacity and the sublevel sets of the Green's function. This is joint work with Xin Dong (University of Connecticut) and Yuan Zhang (Purdue University Fort Wayne). |
|
| Date: | December 2, 2021 |
| Time: | 2:00pm |
| Location: | Zoom |
| Speaker: | Anne-Katrin Gallagher, Gallagher Tool and Instrument |
| Title: | On the dimension of bundle-valued Bergman spaces on P^1 |
| Abstract: | We give potential-theoretic characterizations of the dimension of any line-bundle-valued Bergman space on an open subset in $\mathbb{P}^1$. This is joint work with Purvi Gupta and Liz Vivas. |
|
Menu