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WKB, Opers, and Limiting Configurations
Mathematical Physics Seminar| Speaker: | Richard A. Wentworth, University of Maryland |
| Related Webpage: | https://www.math.umd.edu/~raw/ |
| Location: | 2112 MAB |
| Start time: | Fri, Nov 1 2019, 11:00AM |
The moduli space of $SL(2)$ Higgs bundles on a closed Riemann surface is a hyperkähler variety homeomorphic to the space of $SL(2)$ flat connections. The end of the moduli space is parametrized by "limiting configurations" that are related to asymptotic spectral data for the Higgs bundle. Motivated by results in the exact WKB analysis of the Schrödinger equation, we will discuss the limiting behavior of complex projective structures (or "Opers"). A bridge between the various points of view is provided by Thurston's notion of a "pleated surface". This is joint work with Andreas Ott, Jan Swoboda, and Michael Wolf.