Title: ALG Gravitational Instantons and Hitchin Moduli Spaces
Abstract: Four-dimensional complete hyperkaehler manifolds can
be classified into ALE, ALF, ALG, ALG*, ALH, ALH* families. It has
been conjectured that every ALG or ALG* hyperkaehler metric can be
realized as a 4d Hitchin moduli space. I will describe ongoing work
with Rafe Mazzeo, Jan Swoboda, and Hartmut Weiss to prove a special
case of the conjecture, and some consequences. The hyperkaehler
metrics on Hitchin moduli spaces are of independent interest, as the
physicists Gaiotto-Moore-Neitzke give an intricate conjectural
description of their asymptotic geometry.