Gravitational instantons, rational surfaces, and K3 surfaces

Seminar: 
Geometric Analysis and Application
Event time: 
Friday, March 4, 2022 - 2:00pm
Speaker: 
Jeff Viaclovsky
Speaker affiliation: 
University of California at Irvine
Event description: 

Abstract:

I will describe some examples of complete non-compact Ricci-flat metrics in dimension 4, which are called “gravitational instantons.” In many cases, these can be compactified complex analytically to rational surfaces. I will then discuss how these gravitational instantons can arise from sequences of degenerating Ricci-flat metrics on the compact K3 surface, through a process called “bubbling”.