The universal structure of moment maps in complex geometry

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 discuss a more basic question: what is the recipe to actually produce interesting geometric PDEs in complex geometry? The construction will be geometric, using a combination of universal families and tools from equivariant differential geometry. This is joint work with Michael Hallam.

Ruadhaí Dervan

University of Glasgow

I'm a Senior Lecturer and Royal Society University Research Fellow at the University of Glasgow. I've previously spent parts of my career and education at the University of Cambridge (where I was a fellow of Gonville & Caius College), École Polytechnique, Université libre de Bruxelles and Trinity College Dublin.

I research complex geometry, which is roughly the intersection of algebraic and differential geometry. I'm interested in both the analytic and algebro-geometric sides of complex geometry, and at the moment most of my work lies somewhere between the two. Topics I'm currently interested in include Kähler geometry, K-stability, moduli theory, non-Archimedean geometry and geometric analysis, amongst others.