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

Basic Notions: Jake Solomon "Geometric stability"

Date: 
Thu, 19/11/202016:00-17:15

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