The universal structure of moment maps in complex geometry

Ruadhaí Dervan (University of Glasgow)

Monday 23rd January, 2023 16:00-17:00 Maths 311B

Abstract

Much of complex geometry is motivated by linking the existence of solutions to geometric PDEs (producing "canonical metrics") to stability conditions in algebraic geometry. I will answer a more fundamental question: what is the recipe to produce geometric PDEs in complex geometry? The solution to this will use some old tools from symplectic geometry, namely equivariant differential geometry and the theory of moment maps. I will not assume any prior knowledge of complex or symplectic geometry. This is joint work with Michael Hallam.

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