Harder-Narasimhan stratifications for decorated principal bundles

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• Daniel Halpern-Leistner (Cornell University)
• Wednesday 19 June 2024, 15:30-16:30
• Seminar Room 1, Newton Institute.

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EMGW05 - Moduli stacks and enumerative geometry

Harder-Narasimhan (HN) theory gives a structure theorem for principal G bundles on a smooth projective curve. 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 algebraic stacks, I will discuss work with Andres Fernandez Herrero applying this general machinery to the stack of maps from a curve C to a quotient stack X/G, where G is a reductive group and X is an affine G-scheme. Our main immediate application is to compute generating functions for K-theoretic gauged Gromov-Witten invariants. The method we develop to analyze this moduli problem is an infinite dimensional analog of geometric invariant theory, which is potentially applicable to a much broader range of moduli problems.

This talk is part of the Isaac Newton Institute Seminar Series series.

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