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In the mid-1980s, Hitchin introduced an interesting non-linear partial differential equation on a Riemann surface called the Hitchin equation as a dimensional reduction of the ASD connections. Solutions of the equation are called harmonic bundles. Since then, much exciting research has been done on harmonic bundles on compact Riemann surfaces. One of the fundamentals is the theorem of Hitchin and Simpson about the equivalence between harmonic bundles and Higgs bundles. Their theorem implies, among other things, the existence of a non-commutative deformation of any spectral curve over a compact Riemann surface.

This talk will discuss a generalization to harmonic bundles on non-compact Riemann surfaces based on the joint work with Qiongling Li.

There will be a reception from 3-3:50 PM following the talk, also in 1147 MSB. Professor Mochizuki's visit is supported by NSF-FRG: Collaborative Research: Complex Lagrangians, Integrable Systems, and Quantization (DMS-2152257).