Noncommutative Geometry Conference

Celebration of Alexander Efimov's EMS Prize in Mathematics!

In 2020 Alexander Efimov, a Research Fellow at the International Laboratory for Mirror Symmetry and Automorphic Forms (HSE University)  and a Senior Researcher at  the Algebraic Geometry Section of Steklov Mathematical Institute of RAS,  has been awarded by the European Mathematical Society’s Prize.

Join us on the 17th of December on ZOOM  01:30 PM (Moscow time)
MEETING ID. 816 4070 0608

14.00 Dmitry Kaledin (Laboratory of Algebraic Geometry HSE, Steklov Mathematical Institute)

Title: Non-commutative cristalline cohomology

Abstract: I am going to give an overview of the several constructions of non-commutative analogs of cristalline cohomology that appeared recently, with special focus on "linear" constructions of Vologodsky-Petrov and Tsygan. If time permits, I will end with some speculations on what might be possible over R.

16.00 Maxim Kontsevich (IHES) 

Title: Towards dimension theory for spectral semi- orthogonal decompositions 

 Abstract: It is expected that the derived category of coherent sheaves on a smooth projective variety has a canonical semiorthogonal decomposition governed by the generic spectrum of quantum multiplication deformed by algebraic classes. I present a hypothetical formula for the Serre dimension of elementary pieces for complete interesections in projective spaces, and sketch applications to the rationality questions.

17.30 Denis Auroux (Harvard University)

Title: Mirrors of curves and their Fukaya categories

Abstract: The mirror of a genus g curve can be viewed as a trivalent configuration of 3g−3 rational curves meeting in 2g−2 triple points; more precisely, this singular configuration arises as the critical locus of the superpotential in a 3-dimensional Landau-Ginzburg mirror. In joint work with Alexander Efimov and Ludmil Katzarkov, we introduce a notion of Fukaya category for such a configuration of rational curves, where objects are embedded graphs with trivalent vertices at the triple points, and morphisms are linear combinations of intersection points as in usual Floer theory. We will describe the proposed construction of the structure maps of these Fukaya categories, attempt to provide some motivation, and outline examples of calculations that can be carried out to verify homological mirror symmetry in this setting.

YouTube playlist link

Organizing Committee:

Katzarkov Ludmil (NRU HSE, Miami University) 

Orlov Dmitri (Steklov Mathematical Institute of RAS)

Przyjalkowski Victor (NRU HSE, Steklov Mathematical Institute of RAS)

Yakovlev Ivan (NRU HSE)

Institutions:
International Laboratory for Mirror Symmetry and Automorphic Forms, NRU HSE, Moscow 
Steklov Mathematical Institute of Russian Academy of Sciences, Moscow