• • 6/7/2018: Gradient flows, iterated logarithms, and semistability
    
  • 6/6/2018: Categorical Kähler Geometry

June 7, 2018
TITLE: Gradient flows, iterated logarithms, and semistability

ABSTRACT: The formalism of categorical Kähler geometry outlined in the previous lecture leads to the study of certain dynamical systems. A typical example is furnished by the Yang-Mills flow on the space of hermitian metrics on a holomorphic bundle. It turns out that the asymptotic behaviour of these dynamical systems is governed by iterated logarithms. The talk will elaborate on this statement, and explain how it leads to the discovery of a canonical refinement of the Harder-Narasimhan filtration in a variety of contexts. This is a report on joint work with Fabian Haiden, Ludmil Katzarkov, and Maxim Kontsevich.

Slides of lecture

June 6, 2018
TITLE: Categorical Kähler Geometry

ABSTRACT: After introducing the paradigm of derived geometry, I will outline attempts to formalize and understand the mathematical structures underlying the physical notion of stability for D-branes in string theory using the language of derived noncommutative geometry. These efforts build upon Bridgeland’s notion of stability conditions on triangulated categories, and are inspired by ideas from symplectic geometry, non-Archimedean geometry, dynamical systems, geometric invariant theory, and the Donaldson-Uhlenbeck-Yau correspondence. This talk is based on joint work with Fabian Haiden, Ludmil Katzarkov, and Maxim Kontsevich.

Slides of lecture