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Curious q-series and Jacobi Theta functions March 21, 2011 (10:00 AM PDT - 10:50 AM PDT)
Parent Program: --
Location: MSRI: Simons Auditorium
Speaker(s) Robert Rhoades
Description Location:  Simons Auditorium

Title:  Curious q-series and Jacobi Theta functions

Many q-series arising in combinatorics and physics, such as
sum_{n=0}^infty q^(n^2)/(1-q)^2(1-q^2)^2...(1-q^n)^2,
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.
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