## Derived categories and applications

**Professor**: Patrick Le Meur - Université Paris Diderot

**Course load**: 20h

**Period**: July 1 - 12, 2019

**Lectures**: from Monday to Friday, 10-12 am

**Venue**: the course will take place in **room PA07**, on the ground floor of Setor de Ciências Exatas, Centro Politécnico.

**Address**: R. Evaristo F. da Costa, 408 - 3o andar - Jardim das Américas - Curitiba - PR

**Fees**: Free (no registration fee)

All participants will receive a certificate of participation issued by Graduate Program in Mathematics at UFPR

**Audience**: researchers, undergraduate and graduate students in mathematics interested in algebra.

**Abstract**: Derived categories are used in many areas of mathematics. They are particularly useful to understand phenomenons from a larger perspective, to describe categories of interest and to prove efficiently properties of homological nature.

The purpose of these lectures is to introduce the concept of derived category together with the standard theory attached to it, to present classes of examples for which a precise description is affordable, and to discuss various applications in algebra and geometry. The lectures will feature both classical aspects of the theory and recent developments related to the representation theory of finite dimensional algebras.

**List of topics:**

**theory of derived categories**: definition and properties of the derived categories associated to an abelian category; cohomological functors; resolutions; total derived functors; elements of the theory of Keller and Rickard,**classes of examples**: derived categories of hereditary abelian categories with an emphasis on the case of module categories of hereditary algebras and of the category of coherent sheaves over the projective line; derived categories of gentle algebras,**applications of derived categories**: homological duality, categories of Cohen Macaulay modules; elements of the Koszul duality and of the bar-cobar formalism.

## Certificates

Here you find a PDF file with all certificates sorted by the first name.