Joint IAS/PU Number Theory Seminar

In 2017, Radchenko-Viazovska proved a remarkable interpolation result for even Schwartz functions on the real line: such a function is entirely determined by its values and those of its Fourier transform at square roots of integers. We give a new proof of this result, exploiting the fact that Schwartz functions are the underlying vector space of the Weil representation W�. This allows us to deduce the interpolation result from the computation of the cohomology of a certain congruence subgroup of SL2(Z)2(�) with values in W�. This is joint work in progress with Akshay Venkatesh.