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Basic Notions: Jake Solomon "Geometric stability" | Einstein Institute of Mathematics

Basic Notions: Jake Solomon "Geometric stability"

Date: 
Thu, 12/11/202016:00-17:15

Abstract: The study of geometric stability begins with Mumford's geometric invariant theory. The Kempf-Ness theorem establishes a connection between geometric invariant theory and symplectic quotients. An infinite-dimensional analog of the Kempf-Ness theorem leads to a deep connection between algebraic-geometric stability and special metric geometries. Examples of this connection include the work of Donaldson and Uhlenbeck-Yau on the Kobayashi-Hitchin correspondence and work of Yau, Tian, Donaldson, and many others on extremal Kahler metrics. At the frontier of current research lies a conjectural connection between Bridgeland stability conditions for the Fukaya category and special Lagrangianembeddings. I will attempt to survey this line of thought while assuming minimal background.