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Maxim Kontsevich: Lectures

January 13, 2022
TITLE: Enumerative invariants and not so special holonomy

There exists a physically motivated BPS counting in various geometric situations associated with special holonomy.
The counting is usually robust and depends only on the connected component of the moduli spaces of more soft geometric structures.

For example, Gromov-Witten invariants depend only on the connected component of the space of symplectic structures on a given smooth manifold (instead of a Kähler metric). I’ll review definitions of natural weaker structures in several contexts, including DT-invariants for Calabi-Yau 3-folds, for holomorphic Lagrangian submanifolds in hyperkähler manifolds, and in Morse-Novikov theory for holomorphic 1-forms. In the latter case one can calculate algebraically all BPS multiplicities when the charges are rational (which could be not attainable in the more rigid geometry).

Slides of Lecture

January 12, 2021
TITLE: Analyticity and resurgence

I will talk on my recent work with Yan Soibelman on analytic wall-crossing structures, and a hypothetical relation to theory of resurgent series by Jean Ecalle. In particular, our considerations imply the resurgence property of WKB series.

Slides of Lecture