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BPS structures and Riemann-Hilbert problems

Jacopo SCALISE
Institution: 
SISSA Trieste
Schedule: 
Thursday, April 6, 2017 - 14:30
Location: 
A-136
Abstract: 

in this talk, I will go through a recent paper by Tom Bridgeland: https://arxiv.org/abs/1611.03697.A BPS structure is a set of data encoding the output of a Donaldon-Thomas count on a CY3 category. In the paper, the author assigns a natural problem of Riemann-Hilbert type to any BPS structure, and provides an explicit and unique solution in the finite and uncoupled case.This first result paves the way to a formal computation in the (still uncoupled, but not finite) case of BPS invariants for 1-dimensional sheaves in a Calabi-Yau 3fold defined by Joyce and Song. Here, the author presents interesting relations between the family of solutions to the RH problem and the genus 0 contribution of the generating function for the Gromov-Witten invariants of X.

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