Higgs bundles, isomonodromic leaves, and minimal surfaces

**Please note special location**

I will discuss various aspects of the geometry of the joint moduli space and nonabelian Hodge correspondence for Higgs bundles on Riemann surfaces with varying complex structures. Specifically, there are four objects that are related in a surprising way: the isomonodromic distribution, the degeneracy of the hermitian pairing arising from the Atiyah-Bott-Goldman form, the “Kodaira-Spencer” form, and the energy functional for equivariant harmonic maps. I will show how this leads to the existence of pseudo-Kaehler metrics for certain moduli spaces of minimal surfaces, recovering and extending several recent constructions of various authors. This work is part of a collaboration with Brian Collier and Jeremy Toulisse.