Fourier Interpolation and the Weil Representation

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Mathilde Gerbelli-Gauthier, McGill University
Fine Hall 214

Meeting ID:  920 2195 5230

Passcode:    The three-digit integer that is the cube of the sum of its digits.

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 $SL_2(Z)$ with values in $W$. This is joint work in progress with Akshay Venkatesh.