The course is intended to serve as a continuation of the course taught in the fall 2023 semester. We plan to discuss applications of Auslander-Reiten theory to the study of finite-dimensional algebras, in particular hereditary ones. In addition, we will look at so-called quasi-hereditary algebras, which appear in various areas of mathematics. Finally, we will focus on applications of the theory to derived noncommutative geometry. All necessary information will be given during the lectures; for the last part, knowledge of basic algebraic geometry is assumed.

• Torsion pairs and tilting.
• Once again about reflection functors.
• Hereditary algebras.
• Quasi-hereditary algebras.
• Triangulated and derived categories.
• Once again about Auslander-Reiten theory.
• Tilting and Morita equivalence.
• Auslander construction.
• Noncommutative resolution of singularities.
• Geometric realizations.

Lecturer
Fonarev Anton Vyacheslavovich

Financial support
The course is supported by the Ministry of Science and Higher Education of the Russian Federation (the grant to the Steklov International Mathematical Center, Agreement no.  075-15-2022-265).

Institutions
Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
Steklov International Mathematical Center