Speaker: Andreas Malmendier (Colby College)
Title: Gauge theory in four dimensions and mock theta functions.
Abstract:
In the past 30 years gauge theory has been proven to be an important tool in the investigation of four-dimensional manifolds and has played a major role in new developments in both mathematics and physics. In physics, the moduli space of vacua for the topological N=2 supersymmetric pure gauge theories with gauge group SU(2) or SO(3) is the modular curve 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 past work, I proved that its cusp contributions computes the Donaldson invariants of complex projective plane, a conjecture made by Moore and Witten. I will also explain how string theory suggests a connection of this construction to a generalized elliptic genus and the umbral moonshine conjecture.