Algebraic Geometry Seminar: "Integrality of instanton numbers"

Speaker: Masha Vlasenko, Institute of Mathematics of the Polish Academy of Sciences in Warsaw

Abstract: In 1991 physicists Candelas, de la Ossa, Green and Parkes predicted that numbers of rational curves of fixed degree on the generic quintic threefold are equal to so called instanton numbers, calculated in terms of solutions of a differential equation on its 'mirror manifold'. By construction, these numbers are rational, however it was observed in numerous examples that instanton numbers turn out to be integers. In 2002 Stienstra outlined an approach to integrality using the p-adic Frobenius structure on the differential equation. In this talk I will explain what the Frobenius structure is and show its rather elementary construction, which allows us to prove integrality of instanton numbers in some key examples of mirror symmetry. This is joint work with Frits Beukers.

Host: Matt Kerr