Georg Oberdieck (MIT), The Igusa cusp form conjecture

Abstract: I will explain recent work with Aaron Pixton and Junliang Shen which yields a proof of the Igusa cusp form conjecture. The conjecture says that the Donaldson-Thomas invariants of the product of a K3 surface and an elliptic curve are the coefficients of a Siegel modular form, the reciprocal of the Igusa cusp form. The proof uses a combination of sheaf theoretic methods (in particular derived autoequivalences) (with J. Shen) and new results in the Gromov-Witten theory of elliptic fibrations (with A. Pixton).