Convolution sums from Trace Formulae

Previously we found certain convolution sums of divisor functions arising from physics yield Fourier coefficients of modular forms. In this talk we will discuss the limitations of the current proof of these formulas. We will also explore the connection with the Petersson and Kuznetsov Trace Formulae and the possibility of extending these formulas to other cases. The work mentioned in this talk is in collaboration with Ksenia Fedosova, Stephen D. Miller, Danylo Radchenko, and Don Zagier.