Gromov–Witten and Donaldson–Thomas invariants are enumerative invariants that can be defined for a Calabi–Yau threefold X. Whereas the GW invariants count stable holomorphic maps from a complex curve into X, the DT invariants count coherent sheaves supported on a holomorphic curve in X subject to some stability condition. Although superficially different, it has been conjectured by Maulik–Nekrasov–Okounkov–Pandharipande that the two sets of invariants contain the same information. In this talk, we shall be exploring a realisation of this conjectural equivalence inspired by topological string theory wherein the DT invariants appear as Stokes data associated to Borel resummations of the generating function of the GW invariants, at least in the case where X is the resolved conifold. In particular, we will find in this case that all the Borel resummations are transformations of the triple sine function studied in a recent work of Bridgeland. Finally, we will be seeing how the ambiguity from Borel resummations has a natural geometric interpretation in context of the c-map construction in supergravity. All of this is based on the arXiv preprints 2109.06878 with Murad Alim, Jörg Teschner, and Iván Tulli; 2106.11976 with Murad Alim and Iván Tulli; and 2103.05060 with Mauro Mantegazza (to appear in Geometriae Dedicata).
ICTS Math-Phys seminar is a virtual seminar at the intersection of mathematics (geometry, algebra, representation theory, higher categories, TQFT, ...) and theoretical physics (QFT, string theory, condensed matter, ...). The purpose of this series is to bring together mathematicians and physicists around topics of common interest and foster interdisciplinary discussions.
For joining the mailing list for announcements and Zoom links, please fill out this form .