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Number Theory Seminar

Fourier Interpolation and the Weil Representation

Mathilde Gerbelli-Gauthier (McGill University)

Location:  Hill 525
Date & time: Tuesday, 26 March 2024 at 2:00PM - 3:00PM

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) with values in 𝑊. This is joint work with Akshay Venkatesh.

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