GP seminar: The refined local Donaldson-Thomas theory of curves

Abstract: The Maulik-Nekrasov-Okounkov-Pandharipande correspondence predicts an equivalence between the partition functions of (numerical) Gromov-Witten and (numerical) Donaldson-Thomas invariants of compact threefolds. It was recently proposed by Pardon a solution of this conjectural correspondence by reducing to the simpler case of local curves, which are more amenable for computations by means of TQFT methods. Even more recently, inspired by the seminal work of Nekrasov-Okounkov on the index in M-theory, Brini-Schuler proposed a refined GW/DT correspondence. In this talk, I will present a full solution for the Donaldson-Thomas side of the refined GW/DT correspondence in the case of local curves. In particular, I will explain how to derive the refined DT partition function without relying on degeneration techniques and TQFT methods, and how our formulas recover string-theoretic prediction of Aganagic-Schaeffer.

This is a seminar in the Centre of Geometry and Physics seminar series.