# Dr. Murad Alim, Universität Hamburg: "BPS variation of Hodge structure "

Jan 22, 2019 from 02:15 PM to 03:45 PM

LMS 4 - Raum 312 - Diskussionsraum

Abstract:

The study of BPS states in families of supersymmetric quantum field theories has been a fruitful source of interaction between mathematics in physics. Mathematically, BPS states of a given physical theory correspond to stable coherent sheaves on a Calabi-Yau (CY) threefold or to special Lagrangian submanifolds of the mirror CY. It is central to the study of BPS states that their stability conditions can be varied leading to wall-crossing phenomena. In this talk, I will first review how quiver representation theory can be used to study BPS states and then discuss a geometric realization of BPS states as trajectories of constant phase of a meromorphic quadratic differential on a Riemann surface. A variation of Hodge structure can be associated to this setup and allows one to formulate wall-crossing phenomena in terms of VHS data. This is based on joint work with Florian Beck and Anna Biggs.