Coordinates: Thursday, 9 June, 15:15-16:15, Room 312 in the Mathematics Building
Speaker: Christian Zickert (Berkeley)
Title: Chern-Simons theory and hyperbolic volume
Abstract: We give a simplicial formula for the Chern-Simons invariant of a flat SL(n,C)-connection (with unipotent holonomy near the boundary) on a compact 3-manifold. Concrete computations reveal the striking new phenomenon that the imaginary part is often (conjecturally always) an integral linear combination of volumes of hyperbolic manifolds. The formula makes use of the extended Bloch group, an object introduced by Walter. This is joint work with Stavros Garoufalidis and Dylan Thurston.