Principal Bundles, Moduli Spaces, Landlands Duality and Motives

I will introduce the notion of a principal bundle. After discussing some recent general results about principal bundles, I will define the so-called Hitchin integrable system. In the simplest case, the Hitchin systems boils down to the description of a diagonalizable linear operator via the sets of its eigenspaces and eigenvalues. I will formulate the conjectural Langlands duality for Hitcihn systems. After giving a survey of the current state of the conjecture, I will speculate on how one can use motivic classes to approach the conjecture.

The speaker is a candidate for a position in the Department.