Description
Speaker: Pranav Pandit
Date & Time: 6 February, 3pm
Venue: Room 215
Title: Categorical Kähler Geometry: from derived categories to dynamical
systems
Abstract:Mirror symmetry is a phenomenon predicted by string theory in
physics.
It allows one to translate questions in symplectic geometry to questions
in complex geometry, and vice versa. The homological mirror symmetry
program interprets mirror symmetry within the unifying categorical
framework of derived noncommutative geometry. After introducing these
ideas, I will describe an approach to a theory of Kähler metrics in
derived noncommutative geometry. We will see how this leads to (i) a
non-Archimedean categorical analogue of the Donaldson-Uhlenbeck-Yau
theorem, inspired by symplectic geometry, and (ii) the discovery of a
refinement of the Harder-Narasimhan filtration which controls the
asymptotic behavior of certain geometric flows. This talk is based on
joint work with Fabian Haiden, Ludmil Katzarkov, and Maxim Kontsevich.