Time：8:30-9:30, Thursday, July 24 2025
Zoom ID: 915 2857 6617
Passcode: 767029
Speaker：Phil Harrington, University of Arkansas
Title：Sobolev Regularity for the Bergman Projection in Complex Manifolds
Abstract：The Bergman Projection associated to a domain in a complex manifold is the orthogonal projection from the space of L^2 functions on the domain to the space of L^2 holomorphic functions on that domain. On a domain in complex Euclidean space, the question of whether the Bergman Projection is continuous in a given Sobolev space is a significant question with a rich history. In complex manifolds, domains can be constructed with properties that are impossible in Euclidean space, such as a relatively compact Stein domain with a compact Riemann surface in its boundary. We will survey the relevant results in Euclidean space and then look at some examples and recent results on domains in complex manifolds.
