Monday

Gravitational instantons are defined as non-compact, non-flat, complete hyperkähler 4 manifolds with L^2 curvature decay. They have been recently classified, and all arise as bubbling limits of K3 surfaces. The Modularization Conjecture posits that any gravitational instanton arises as the moduli space of gauge-theoretic equations.

In this talk, I'll focus on a special kind of gravitational instanton: ALG D_4 gravitational instantons. These can be conjecturally realized as moduli spaces of Hitchin's equations, a system of gauge-theoretic equations on a Riemann surface that is recognized as a central object in mathematics. In joint work (arXiv:2603.17020) and ongoing work with Rafe Mazzeo, Jan Swoboda, and Hartmut Weiss, we prove the Modularization Conjecture in this case.