Speaker: Alexander Goncharov (Yale University)

Abstract: The second motivic Chern class is the generator of the degree 4, weight 2 motivic cohomology of BG, where G is a split simple algebraic group over Q. I will construct a collection of explicit cocycles for the second motivic Chern class.
It has a number of applications, such as local combinatorial formulas for the usual second Chern class of a G-bundle over a manifold,
or   explicit constructions of the determinant bundle on Bun(G),  the extension of G by K_2 etc.
The construction is closely related to the cluster structure of the moduli space of decorated G-local systems on a   surface S with boundary.