Fourier Interpolation and the Weil Representation
Fourier Interpolation and the Weil Representation

Mathilde GerbelliGauthier, McGill University
Fine Hall 214
Meeting ID: 920 2195 5230
Passcode: The threedigit integer that is the cube of the sum of its digits.
In 2017, RadchenkoViazovska 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 $SL_2(Z)$ with values in $W$. This is joint work in progress with Akshay Venkatesh.