EVENT DETAILS AND ABSTRACT

Title: Tannakian duality for Tannakian categories
Speaker: Marc Hoyois
Speaker Info: Northwestern University
Brief Description:
Special Note:
Abstract:

I will define the notion of Tannakian category and give several examples from various areas of mathematics: representations of groups, local systems on topological spaces, Hodge structures, and, conjecturally, motives (this last example motivated the invention of Tannakian categories by Grothendieck). Tannakian duality (in this context) states that any Tannakian category is the category of representations of a unique affine group scheme, called the fundamental group of the category; this generalizes both the fundamental group of a space and the Galois group of a field extension. I will exhibit the fundamental groups of my examples. If time allows I will say something about the proof of Tannakian duality, due to Saavedra and Deligne.