Constructions and Applications of Mock Modularity at Depth Two

Abstract: False and mock modular forms along with their higher depth generalizations make their appearance in mathematical physics and geometry in contexts such as Vafa-Witten invariants or Z-hat invariants of three manifolds. In this talk I will describe the interaction between various constructions of these objects and their Fourier coefficients by focusing on a particular example involving rank 2 Vafa-Witten invariants. In particular, I will demonstrate a Hardy-Ramanujan-Rademacher type exact formulae for these Vafa-Witten invariants along with a twofold Eisenstein series construction for the pure component of the generating function. In particular, the latter construction leads to nontrivial identities for the Fourier coefficients of the aforementioned depth two mock modular forms, which have expressions as indefinite theta series derived from the wall-crossing formula. This is based on earlier as well as ongoing work with K. Bringmann.

mathematical physicsalgebraic geometrygeometric topology

Audience: researchers in the topic

Richmond Geometry Meeting 2024

Series comments: The Richmond Geometry Meeting will focus on emergent research topics while bringing together researchers in algebraic geometry, low-dimensional topology, and mathematical physics. In summer 2024, we will highlight developments in Geometric Topology and Moduli.

Zoom meeting id: 835 6496 8395 password: RGMVCU2024