Subscribe to Events

Abstract: Gravitational instantons are defined as non-compact non-flat complete hyperkahler 4-manifolds with L^2 curvature decay.  They have been recently classified and all arise as bubbling limits of K3 surfaces.  The Modularity Conjecture posits that any gravitational instantons 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 are recognized as a central object in mathematics. In joint work https://arxiv.org/abs/2603.17020. Click or tap if you trust this link.">2603.17020 and ongoing work with Rafe Mazzeo, Jan Swoboda, and Hartmut Weiss, we prove the modularity conjecture in this case.