Abstract:

Gravitational instantons are defined as non-compact non-flat complete hyperkaehler 4-manifolds with L^2 curvature decay. These have been recently classified and all arise as bubbling limits of K3 surfaces.

It is conjectured that all 4d gravitational instantons arise as hyperkaehler metrics on gauge theoretic moduli spaces. In this talk, I’ll focus on a special kind of gravitational instantons called ALG 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 this talk, I’ll discuss recent work towards conjecture in the specific case of ALG-D4 gravitational instantons via Hitchin moduli spaces on the four-punctured sphere.

This talk is based on joint work with Rafe Mazzeo, Jan Swoboda, and Hartmut Weiss in 2603.17020.