Topological recursion, exact WKB analysis, and the (uncoupled) BPS Riemann-Hilbert problem (Omar Kidwai, Birmingham)

21.11.2023 15:00 – 17:00

The notion of BPS structure describes the output of the Donaldson-Thomas theory of CY3 triangulated categories, as well as certain four-dimensional N=2 QFTs. Bridgeland formulated a certain Riemann-Hilbert-like problem associated to such a structure, seeking functions in the ℏplane with given asymptotics whose jumping is controlled by the BPS (or DT) invariants, which appear in the description of certain complex hyperkahler manifolds.
To solve a totally different problem in physics, Chekhov and Eynard-Orantin introduced the topological recursion, which takes in very similar initial data and recursively produces an infinite tower of geometric objects, which have been shown to be useful in enumerative geometry.
Starting from the datum of a quadratic differential on a Riemann surface X, I'll briefly recall how to associate a BPS structure to it, and explain, in the simplest examples, how to produce a solution to the corresponding Riemann-Hilbert problem using a procedure called topological recursion, together with exact WKB analysis of the resulting "quantum curve". Based on joint work with K. Iwaki.

Seminar with a break

Lieu

Bâtiment: Conseil Général 7-9

Room 1-07, Séminaire "Groupes de Lie et espaces de modules"

entrée libre