241014 Representations of Algebras II (V) (WiSe 2025/2026)

I want to cover a number of key topics in the representation theory of finite-dimensional associative algebras:

Correspondences given by faithfully balanced modules, and applications to Auslander algebras and homological conjectures. (Originally planned for the previous semester, but carried over, since there was not enough time.)

Tilting and tau-tilting theory, including equivalences of derived categories.

Geometric methods for studying representations of algebras, including relevant facts about varieties and schemes without proofs. (There will be less time for this than originally planned.)

If time, possibly preprojective algebras and Kleinian singularities.

Teilnahmevoraussetzungen, notwendige Vorkenntnisse

Students are expected to have some familiarity with rings and modules, and topics such as categories, projective and injective modules, and Ext groups. I will freely use ideas and results from the previous course in the sequence "Representations of Algebras".

Externe Kommentarseite

https://www.math.uni-bielefeld.de/~wcrawley/2526RAII/