Algebraic Geometry Seminar: Ben Davison (Oxford)

I will describe recent work on motivic DT invariants for 3-manifolds, which are expected to provide a refinement of Chern-Simons theory. The conclusion will be that these should be possible to define and work with, but there will be some interesting problems along the way. There will be a discussion of the problem of upgrading the description of the moduli space of flat connections as a critical locus to the problem of describing the fundamental group algebra of a 3-fold as a "noncommutative critical locus," including a result regarding topological obstructions for this problem. I will also address the question of whether a motivic DT invariant may be expected to pick up a finer invariant of 3-manifolds than just the fundamental group.