# Kontsevich-Soibelman wall-crossing formula and a Riemann-Hilbert problem

## Connections for Women: Holomorphic Differentials in Mathematics and Physics August 15, 2019 - August 16, 2019

**Speaker(s):**Anna Barbieri (University of Sheffield)

**Location:**SLMath: Eisenbud Auditorium

**Tags/Keywords**

Riemann-Hilbert problem

Donaldson-Thomas theory and BPS numbers

**Primary Mathematics Subject Classification**No Primary AMS MSC

**Secondary Mathematics Subject Classification**No Secondary AMS MSC

#### 07-Barbieri

The goal of this talk is to present the wall-crossing formula (WCF) introduced by Kontsevich and Soibelman and a class of Riemann-Hilbert problems naturally associated. The WCF describes a special behaviour of some counting invariants depending on a parameter space in a piece-wise constant way. I will recall how this formula appears with an explicit example of a moduli space of quadratic differentials and I will present the solution of a simple instance of the Riemann-Hilbert problem.

#### 07-Barbieri

H.264 Video | 894_27296_7864_07-Barbieri.mp4 |

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