Title: Mirror symmetry and smoothing surface singularities

Speaker: Mark Gross

Time: May, 20th, 9:00-10:00

Abstract: I will talk about joint work with Paul Hacking and Sean Keel, which gives a general construction of a mirror family to any pair (Y,D) where Y is a rational surface and D is an anti-canonical cycle of rational curves. In the case that D is contractible to a cusp singularity, the mirror family provides a smoothing of the so-called dual cusp singularity, hence proving a 1981 conjecture of Looijenga on smoothability of cusp singularities. Our construction has many other applications as well.