• Speaker: Rafe Mazzeo
• Time: 2:00-3:00
• Abstract: The natural metric on the moduli space of solutions to the Hitchin equations on a Riemann surface is hyperkaehler. On the four-punctured sphere, this moduli space is in fact a 4-dimensional gravitational instanton of ALG type. A long-standing question asks whether all gravitational instantons arise as gauge-theoretic moduli spaces (or similar finite dimensional analogues). I will explain how and why this is true in this particular setting, namely that the available parameters in the Hitchin construction exhaust the full moduli of ALG metrics of D4 type. Joint with Fredrickson, Swoboda, Weiss.