# Degenerations of K3 Surfaces, Gravitational Instantons, and M-Theory

Sponsor(s): Physics

The detailed study of degenerations of K3 surfaces as complex manifolds

goes back more than forty years and is fairly complete. Much less is

known about the analogous problem in differential geometry of finding

Gromov--Hausdorff limits for sequences of Ricci-flat metrics on the K3

manifold. I will review work of H.-J. Hein and G. Chen--X. Chen on

gravitational instantons with curvature decay, and describe applications

to the K3 degeneration problem. I will also review some very recent work

of Hein-Sun-Viaclovsky-Zhang constructing some additional important

examples. The known examples are connected to physical dualities, as I

shall also explain.

Type: PANEL/SEMINAR/COLLOQUIUM

Contact: Travis Maxfield