Electromagnetism on a Riemann surfaces

Nov 2021

talk expository slides

Summary:

Maxwells equations have a very elegant formulation in terms of differential forms. As a U(1) gauge theory, the electromagnetic field is a connection on a U(1) principle bundle. These are equivalent to holomorphic line bundles! The moduli space of solutions to vacuum maxell’s equations on a riemann surface is the Jacobian. We can give much of classical Riemann surface theory a gauge-theoretic coat of paint. This observation, generalized to nonableian groups and noncompact groups, is the heart of the nonabelain hodge correspondence.

Presented at:

MATH669, Riemann surfaces, UMD, Fall 2021