Jan Manschot, Trinity College Dublin
Title: Gauge theory and generalized Appell functions
Abstract: Appell functions are q-series which play a central role in recent developments of (mock) modular forms. I will discuss how Appell functions appear in the study of partition functions of N=4 supersymmetric gauge theories on 4-manifolds. Using algebraic-geometric techniques, the physical partition functions can be determined explicitly as generating functions of invariants of moduli spaces of vector bundles. These generating functions may be expressed in terms of Appell functions if the rank of the vector bundle is 2, or, for rank > 2, provide a higher dimensional generalization of Appell functions. In joint work with Bringmann and Rolen, we recently proved identities for generalized Appell functions based on the A_2 root lattice.