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The asymptotic geometry of the Hitchin moduli space

Student-Run Geometry/Topology Seminar

Speaker: Laura Fredrickson, Stanford University
Location: MSB 3106
Start time: Tue, Nov 12 2019, 11:00AM

Hitchin's equations are a system of gauge theoretic equations on a Riemann surface that are of interest in many areas including representation theory, Teichmuller theory, and the geometric Langlands correspondence. The Hitchin moduli space carries a natural hyperkahler metric. A conjectural description of its asymptotic structure appears in the work of physicists Gaiotto-Moore-Neitzke. I will discuss a recent series of results on the asymptotic geometry, culminating in a proof of a weak form of Gaiotto-Moore-Neitzke's conjecture. As an application, I'll talk about recent work constructing K3 surfaces metrics by gluing together Hitchin moduli spaces.