This $307,873 Project Grant from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) will fund research into geometric, analytic, and algebraic aspects of real submanifolds in complex varieties and their symmetries from June 1, 2022 to May 31, 2025. The University of California, San Diego will study properties of various metrics and kernels related to Kähler-Einstein metrics on higher-dimensional spaces, with goals of characterizing domains and complex manifolds. Additional aims include understanding conditions for the Bergman metric on a domain to be Kähler-Einstein if and only if the domain is biholomorphically equivalent to the ball, as well as considering existence and regularity questions for CR maps between generic submanifolds of infinite type. Findings are expected to enhance understanding of the role of invariant objects and symmetries in several complex variables and complex geometry, with potential utility in physical models and applications.
Generated 1/7/24, 2:28 AM