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The Asymptotic Geometry of the Hitchin Moduli Space

[HYBRID WORKSHOP] Connections Workshop: Analytic and Geometric Aspects of Gauge Theory August 25, 2022 - August 26, 2022

August 26, 2022 (09:30 AM PDT - 10:30 AM PDT)
Speaker(s): Laura Fredrickson (University of Oregon)
Location: SLMath: Eisenbud Auditorium, Online/Virtual
Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC
Video

The Asymptotic Geometry Of The Hitchin Moduli Space

Abstract

Hitchin's equations are a system of gauge theoretic equations on a Riemann surface that are of interest in many areas including representation theory, Teichm\"uller theory, and the geometric Langlands correspondence. The Hitchin moduli space carries a natural hyperk\"ahler metric.  An intricate conjectural description of its asymptotic structure appears in the work of Gaiotto-Moore-Neitzke and there has been a lot of progress on this recently.  I will discuss some recent results using tools coming out of geometric analysis which are well-suited for verifying these extremely delicate conjectures. This strategy often stretches the limits of what can currently be done via geometric analysis, and simultaneously leads to new insights into these conjectures.

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The Asymptotic Geometry Of The Hitchin Moduli Space

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