Course by L.Katzarkov

There will be an introductory course by L. Katzarkov starting Sept 8 14:00 at HSE 

The course will contain introduction to these topics: 
• LG models and novel structures associated with them 3 lectures
• Perverse sheaves of categories 2 lectures 
• Perverse sheaves of stability conditions 3 lectures 
• Central manifolds and spectral networks 3 lectures 
• Categorical Seiberg - Whitten invariants 1 lecture.
These new invariants are being developed in collaboration with V. Golishev, S. Galkin, A. Fonarev, V. Prizhalkovskiy, A. Efimov.

29.09.17 (Friday), 14:00, room 110. Fukaya Seidel Categories

In the previous lectures many examples of exceptional collections were considered. Most of the examples were derived categories of coherent sheaves of smooth projective varieties. In this talk ( and several consecutive talks) after defining Homological Mirror Symmetry we will look at A side partners and define Fukaya Seidel categories.  The notion of perverse sheaves of categories will be introduces as well.

13.10.17, 20.10.17 (Friday), 14:00, room 110.  Mirror symmetry for del Pezzo surfaces.
I will discuss two directions of homological mirror symmetry for del Pezzo surfaces as well as some beyond-homological extensions, such as a structure of cluster variety on mirror dual surface.

27.10.17 (Friday), 14:00, room 110. Landau--Ginzburg models for Fano manifolds - I

In this talk we will describe Landau--Ginzburg models of Del Pezzo surfaces, relations between them, and their properties.

3.11.17 (Friday), 14:00, room 110. Landau--Ginzburg models for Fano Manifolds II

In this talk we will describe Landau--Ginzburg models of some Fano threefolds and complete intersections, relations between them, and their properties.

10.11.17 (Friday), 14:00, room 110. Moduli space of LG models, Stability conditions and Diophantine equations.

In this talk we will outline a shamefully arrogant and rather provocative approach to an old conjecture by Markov.

The approach is based on recent developments and it seems to  point out to a general phenomenon.

17.11.17 (пятница), 14:00, ауд. 110. Basic examples of stability conditions on triangulated categories.

I will give some basic intuition on stability conditions on triangulated categories, and illustrate it on the derived categories of representations of quivers and coherent sheaves on smooth projective curves.