Henning Krause, Bielefeld University
Thick subcategories for hereditary algebras via non-crossing partitions
Minicourse
March 10-12, 2025
Ca' Vignal 2, Sala Riunioni

Monday, March 10,      16:00-16:45
Tuesday, March 11,      15:30-17:00
Wednesday, March 12, 18:00-18:45

Abstract: The goal of the lectures is to explain a classification result for representations of finite dimensional hereditary algebras, which is completely independent of the representation type. The result is based on a beautiful interplay between homological and combinatorial structures. The lectures provide an introduction to the techniques which are used, including perpendicular calculus and exceptional sequences, Grothendieck groups and Weyl groups, non-crossing partitions etc. The focus will be on concepts and ideas; for full details I will refer to the joint book project with Andrew Hubery.


Andrew Hubery, Bielefeld University
Preprojective algebras of tame hereditary algebras
Minicourse
March 10 and 12, 2025
Ca' Vignal 2, Sala Riunioni

Monday, March 10,      15:00-15:45
Wednesday, March 12, 17:00-17:45

Abstract: The category of regular representations for a tame hereditary algebra decomposes into tubes, say with indexing set X. Using the preprojective algebra we can endow X with the structure of a non-commutative curve, as shown by Baer, Geigle and Lenzing. We will discuss their construction and describe the connections between the geometry of the non-commutative curve, the ring-theoretic properties of the preprojective algebra, and the category of regular modules.