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The ends of the Hitchin moduli space

QMAP Seminar

Speaker: Laura Fredrickson, Stanford
Location: 2112 MSB
Start time: Fri, Jan 19 2018, 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. In this talk, I'll describe what solutions of SL(n,C)-Hitchin's equations ``near the ends'' of the moduli space look like, and the resulting compactification of the Hitchin moduli space. Wild Hitchin moduli spaces are an important ingredient in this construction. This construction generalizes Mazzeo-Swoboda-Weiss-Witt's construction of SL(2,C)-solutions of Hitchin's equations where the Higgs field is ``simple.''