The geometric Weil representation

This is a sequel to Lecture I (given in the algebra seminar, Tuesday). It will be slightly more specialized. The finite Weil representation is the algebra object that governs the symmetries of the Hilbert space H =C(Z/p): The main objective of this talk is to introduce the geometric Weil representation which is an algebra-geometric (l-adic perverse

Weil sheaf) counterpart of the finite Weil representation. Then, I will explain how the geometric Weil representation is used to prove the main technical results stated in Lecture I. In the course, I will explain the Grothendieck geometrization procedure by which sets are replaced by algebraic varieties and functions by sheaf theoretic objects. This is a joint work with R. Hadani (Austin).