Number theory seminar Javier Fresan

Title: Equidistribution of exponential sums on algebraic groups.

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Abstract: I will present a joint work with Arthur Forey and Emmanuel Kowalski in which we prove a general theorem about the equidistribution of discrete Fourier transforms of trace functions of perverse sheaves on commutative algebraic groups over finite fields. In order to make this equidistribution result concrete for a given trace function, one needs to compute a tannakian fundamental group associated with the corresponding perverse sheaf, which can in general be challenging. I will show a family of examples in which this can be done using tools from representation theory (Larsen's alternative) and combinatorics (Sidon sets). If time permits, I will also mention a recent application to graph theory obtained in collaboration with Yuval Wigderson.