Infinite dimensional geometric invariant theory and gauged Gromov-Witten theory

Abstract: Harder-Narasimhan (HN) theory gives a structure theorem for holomorphic vector bundles on a Riemann surface. A bundle is either semistable, or it admits a canonical filtration whose associated graded bundle is semistable in a graded sense. After reviewing recent advances in extending HN theory to arbitrary moduli problems in algebraic geometry I will discuss work in progress with Andres Fernandez Herrero and Eduardo Gonzalez to apply this general machinery to the moduli problem of gauged maps from a curve C to a G-variety X, where G is a reductive group. Our main immediate application is to use HN theory for gauged maps to compute generating functions for K-theoretic gauged Gromov-Witten invariants. This problem is interesting more broadly because it can be formulated as an example of an infinite dimensional analog of the usual set up of geometric invariant theory, which has applications to other moduli problems.

differential geometrymetric geometry

Audience: researchers in the discipline

Western Hemisphere colloquium on geometry and physics

Series comments: Description: Biweekly colloquium of geometers and physicists

This weekly online colloquium features geometers and physicists presenting current research on a wide range of topics in the interface of the two fields. The talks are aimed at a broad audience. They will take place via Zoom on alternate Mondays at 3pm Eastern, noon Pacific, 4pm BRT. Each session features a 60 minute talk, followed by 15 minutes for questions and discussion. You may join the meeting 15 minutes in advance. Questions and comments may be submitted to the moderator via the chat interface during the talk, or presented in person during the Q&A session. These colloquia will be recorded and will be available (linked from the website) asap after the event.