Graduate Student Seminar - Félix Baril Boudreau (Math)

Dear Graduate Students,

You are all invited to the third talk this summer of the Graduate Student Seminar this Thursday 1:00-2:00PM via Zoom (meeting ID and password below). Our speaker this week, Félix Baril Boudreau, will talk about Tannaka duality in various contexts.

Speaker: Félix Baril Boudreau

Title: A Glimpse of Tannakian Categories

Abstract: A group is intimately related to its representation theory. For example, a finite abelian group G can be recovered from its group of characters since G is canonically isomorphic to its double dual. The same is true when G is a locally compact abelian topological group by Pontryagin duality. Yet, when G is a locally compact noncommutative group, its irreducible representations don't form a group anymore. Nevertheless, Tannaka was able to reconstruct G from the category of its unitary representations. This gave the Tannaka duality. In the 70's and 80's the Grothendieck school and Deligne worked out a general framework where Tannaka duality holds.

In this talk we will introduce this general context and explain why we have Tannaka dualities for finite groups and affine group schemes. Time permitting, we will briefly discuss a modern take on this theory lead by Katz which allows us for example, to tackle questions of analytic number theory. This theory involves an interesting mixture of perverse sheaves, Fourier transforms and equidistribution problems of the flavor of the Chebotarev density theorem.

This talk will take a bird-eye viewpoint and will aim to focus on the ideas rather than the details. Familiarity with very basic vocabulary of category theory is recommended while knowledge of the basic definitions of representation theory for finite groups is useful but not necessary.

The talk will start at 1pm, so we encourage you to log in to the zoom meeting by 12:55pm.

Hope to see many of you there!

Sincerely,

Graduate Student Seminar Organizing Committee