Danylo Radchenko: Summation formulas and modular forms

Abstract:
I will talk about a class of summation formulas for Schwartz functions on the real line.
As special cases this will cover the classical Poisson summation formula, but also a curious summation formula originally discovered by Guinand. These identities naturally arise in an interpolation problem for Fourier eigenfunctions and can be explicitly described using modular forms for the Hecke theta group and the Gaussian hypergeometric function.