发布时间： 2023-07-03
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Non-commutative and derived geometry of matrix factorizations

Dates: July 3-8, 2023

Venue: Centre of Pure Mathematics, Moscow Institute of Physics and Technology

**Attention! No lectures on Saturday. The schedule is in Moscow time.**

Organisers: Alexey Bondal, Christopher Brav, Huijun Fan

**Mini-courses:**

Christopher Brav: *Non-commutative geometry of DG categories and Hochschild (co)homology*

Alexander Pavlov: *Matrix factorisations and Cohen-Macaulay modules*

Artem Prikhodko: *Derived algebraic geometry *

**Special lectures:**

Aleksey Bondal: *Non-commutative deformations of functors between abelian categories*

We shall discuss the deformation theory over a non-commutative base of a collection of objects in an abelian category or more generally the deformation theory of faithful functors between abelian categories. We discuss the existence of the universal noncommutative deformation and of a noncommutative Artin stack of the deformation functor.

Boris Shoikhet: *What do dg (bi)categories form? *

Let C,D be small dg categories, there is the dg category Fun(C,D) whose objects are dg functors, and a morphism F—>G is a complex "of natural transformations". Then, when C runs through small dg categories, it gives rise to a strict dg 2-category. The drawback of Fun(C,D) is that a quasi-equivalence C—>C' or a quasi-equivalence D—>D' changes the homotopy type of Fun. There is a better homotopy invariant definition, where the morphisms F—>G are given by suitable Hochschild cochain complexes. However, after this is done, the category of small dg categories fails to be a strict 2-category. The question "What do dg categories form?" refers to the question of finding a weak 2-categorical structure there. We'll discuss a solution to this question, due to Tamarkin, in terms of an action of a 2-operad. (It will be the biggest part of the talk). As well, we'll discuss our work on the similar question for (small) dg bicategories (in particular, dg monoidal categories) in place of dg bicategories.

The summer school will be hosted by the Centre of Pure Mathematics at the Moscow Institute of Physics and Technology. The school is aimed at advanced students and post-docs.

Those interested in attending should fill out the registration form

Any questions should be addressed to cpmsummerschool2023@yandex.ru