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.

differential geometry

Audience: researchers in the topic

B.O.W.L Geometry Seminar