From special functions to stability conditions

Abstract: The Gamma function studied by Bernoulli appear all over mathematics and in particular whenever we study special contour integrals. We will review a class of special functions called Barnes multiple Gamma functions that generalize the Gamma function and we will see how they appear in the study of a class of Bridgeland stability conditions with a very simple Donaldson-Thomas (DT) theory. This goes through solving a Riemann-Hilbert-Birkhoff boundary value problem induced by the wall-crossing formula for DT counting invariants, and involving factors that look like cluster transformations. Based on a joint work with T. Bridgeland and J. Stoppa.

mathematical physicscommutative algebraalgebraic geometrycombinatoricsquantum algebrarings and algebrasrepresentation theory

Audience: researchers in the topic

Online Cluster Algebra Seminar (OCAS)