|Location:||MSRI: Simons Auditorium|
Title: Curious q-series and Jacobi Theta functions
Many q-series arising in combinatorics and physics, such as
the partition generating function,
converge for |q|<1 and for |q|>1 and possess a natural boundary for |q|=1.
In the regime |q|<1, such functions are often modular
forms. In the regime |q|>1, these functions fail to be modular but often possess a striking resemblance to modular forms. I will discuss the near modularity of these functions and even
given some meaning to these functions when |q|=1. Such series have played a striking role in Pade Approximation and Quantum Invariants of 3-manifolds.