Abstract : I will outline a logarithmic enhancement of the GromovWitten/Donaldson-Thomas correspondence, with descendants, and study
the behaviour of the correspondence under simple normal crossings
degenerations. I will explain a strong form of the degeneration formula in
logarithmic DT (and GW) theory - the numerical DT invariants of the
general fiber of a degeneration are determined by the numerical DT
invariants attached to strata of the special fiber. As a consequence, we
prove compatibility of the new logarithmic GW/DT correspondence with
degenerations, and in particular, that knowledge of the conjecture on the
strata of the special fiber of a degeneration implies it on the general fiber.
Time permitting, I will try to give a sense for where this recent technical
development puts us in terms of knowledge of the descendant GW/DT
correspondence in general. The talk is based on recent and ongoing joint
work with Davesh Maulik (MIT).
