Abstract:

A major theme of modern complex geometry is the relationship between solvability of geometric PDEs and algebraic stability conditions. The classic example is the Donaldson-Uhlenbeck-Yau theorem, relating the existence of Hermite-Einstein metrics (a special metric on a vector bundle) to the algebraic notion of slope stability. More recently, new PDEs in various geometric settings have arisen through connections with mirror symmetry and string theory. I will describe a new geometric way of deriving large classes of PDEs with automatic connections to algebraic geometry, along with some applications. This involves a geometric approach to the construction of moment maps, which traditionally play a prominent role in symplectic geometry and classical mechanics.

Short bio:

Ruadhaí Dervan is a Professor of Mathematics at the University of Glasgow, where he also holds a Royal Society University Research Fellowship. He was previously based at the University of Cambridge, where he was a Fellow of Gonville & Caius College, and where he finished his PhD in 2016. He is broadly interested in interactions between algebraic and differential geometry, and the use of related ideas in the construction and geometry of moduli spaces in algebraic geometry.