MATH Seminar

Title: Gauge Theory in Four Dimensions and Mock Modular Forms
Seminar: Algebra and number theory
Speaker: Andreas Malmendier of Colby College
Contact: Zachary Kent, kent@mathcs.emory.edu
Date: 2011-01-25 at 3:00PM
Venue: W306
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Abstract: In physics, the moduli space of vacua for the topological N = 2 supersymmetric pure gauge theories with gauge group SO(3) is the universal elliptic curve for the modular group of level 2. Moreover, the supersymmetric gauge theory associates to each four-manifold a not necessarily holomorphic modular form of level two. I will explain why for the complex projective plane this modular form is a Mock theta function - in fact, it is one of the examples listed in Ramanujan's letter to Hardy to undermine a notoriously obscure definition. In joint work with Ken Ono, we then proved that its cusp contributions are the Donaldson invariants of $CP^2$, a conjecture made by Moore and Witten. Time permitting, I will also sketch how string theory suggests a connection of this construction to a generalized elliptic genus.