Dr Justin Trias (University of East Anglia) gives a maths seminar at the School of Mathematics, UEA. The talk is on “Modular Theta Correspondence”. The abstract is below.

The Theta correspondence is an important and somewhat mysterious tool in Number Theory, with arithmetic applications dealing with special values of L-functions, epsilon factors, and local Langlands correspondence. The local variant of the Theta correspondence concerns itself with describing a bijection between prescribed sets of irreducible smooth complex representations of groups G_1 and G_2, where (G_1,G_2) is a reductive dual pair in a symplectic p-adic group. This theory can be extended beyond complex representations to representations with coefficients in any algebraically closed field R as long as the characteristic of R is different from p. However, the correspondence defined in this way may no longer be a bijection, and the question of whether this remains a bijection depends on the characteristic of R and of the size of the G_i.