**Pranav Pandit**

University of Vienna, Austria

September 28, 2017

**From extremal metrics and gradient flows to categorical Kähler geometry**:
This talk is based on joint work with Fabian Haiden, Ludmil Katzarkov, and Maxim Kontsevich. I will describe our attempts to formalize and understand the mathematical structures underlying the physical notion of stability for D-branes in string theory. Our work builds upon Bridgeland?s notion of stability conditions on triangulated categories, and is inspired by ideas from symplectic geometry, non-Archimedean geometry, dynamical systems, geometric invariant theory, and the Donaldson-Uhlenbeck-Yau correspondence.