Максим Смирнов

Максим Смирнов (Augsburg) посетил Лабораторию в ноябре 2017 г. и в феврале-марте 2019 г.

15 ноября 2017 года он выступил с докладом "On Lefschetz exceptional collections and quantum cohomology of Grassmannians" на  еженедельном семинаре Лаборатории.

Abstract: Given a Lefschetz exceptional collection on a variety X one defines its residual subcategory as the orthogonal to the rectangular part of the collection. In this talk we will discuss some (partially) conjectural relations between the quantum cohomology of X and the structure of the residual subcategory in the case of ordinary and symplectic isotropic Grassmannians. The talk is based on joint works, some finished and some still in progress, with A. J. Cruz Morales, S. Galkin, A. Mellit, N.Perrin, and A. Kuznetsov.

1 марта 2019 г. он выступил с докладом "Hochschild cohomology of partial flag varieties" на  еженедельном семинаре Лаборатории.

Abstract: The Hochschild-Kostant-Rosenberg decomposition gives a description of the Hochschild cohomology of a smooth projective variety in terms of the sheaf cohomology of exterior powers of the tangent bundle. In all but a few cases it is a non-trivial task to compute this decomposition, and understand the extra algebraic structure which exists on Hochschild cohomology. I will give a general introduction to Hochschild cohomology and this decomposition, and how this problem can be studied for partial flag varieties (i.e. varieties of the form $G/P$ for $G$ a semisimple algebraic group and $P$ a parabolic subgroup), in particular for the case of maximal parabolic subgroups (i.e. Grassmannians in type A and their analogues in other types). This is joint work in progress with Pieter Belmans.