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Compactifications of Hitchin's moduli space

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Richard Wentworth
University of Maryland/MPIM
Thu, 25/05/2023 - 16:30 - 17:30
MPIM Lecture Hall

The moduli space of rank 2 Higgs bundles has several natural compactifications, depending upon its
algebraic, differential geometric, or topological realizations. In this talk, I will compare the compactification coming from the algebraic geometry of the C-star action with the one coming from the analytic "limiting configurations" of solutions to the Hitchin equations.
I will explain how the nonabelian Hodge correspondence extends as a map between these compactifications. Somewhat surprisingly, the extension is not continuous, but fails in a controlled
way. This is joint work with Siqi He, Rafe Mazzeo, and Xuesen Na.


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