Differential Geometry Seminar: WKB, Opers, and Limiting Configurations

Seminar | December 2 | 3-4 p.m. | 939 Evans Hall

 Richard Wentworth, University of Maryland

 Department of Mathematics

The moduli space of SL(2) Higgs bundles on a closed Riemann surface is a hyperkaehler 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 Schrodinger 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.