The goal of this talk, intended for a broader audience, will be to introduce a class of functions that answer a question in topology, can be computed via analytic methods more common in the theory of dynamical systems, and in the end turn out to enjoy beautiful modular properties of the type first observed by Ramanujan.

Sergei Gukov is currently a professor of theoretical physics and mathematics at the California Institute of Technology, and an external scientific member of the Max-Planck-Institute for Mathematics in Bonn. Professor Gukov is a leading figure in the field of mathematical physics, in particular string theory, gauge theory and topology. He discovered various structures in physics which led to unexpected predictions about the topology of 3- and 4-manifolds and the geometric Langlands program. He was a Clay Mathematics Institute Long Term Prize Fellow in 2001, and was awarded the Sloan Research Fellowship in Science & Technology in 2007.