Event time:
Thursday, April 23, 2015 - 12:15pm to 1:15pm
Location:
431 DL
Speaker:
Paul Hacking
Speaker affiliation:
University of Massachusetts Amherst
Event description:
Andrei Tyurin conjectured the existence of a canonical basis of global sections for an ample line bundle on a K3 surface, analogous to the usual theta functions for abelian varieties. I’ll describe joint work with Gross, Keel, and Siebert where we use ideas from mirror symmetry to prove the conjecture for K3 surfaces near a cusp of the moduli space. The construction is based on the tropicalization of the mirror K3 and its scattering diagram encoding counts of holomorphic discs with Lagrangian boundary conditions.