Seminar Representation Theory, WS 2021/22
Time and place: Wednesdays 10–12 in room V4112
Organisers: Prof. Dr. William CrawleyBoevey, Prof. Dr. Henning Krause, JanPaul Lerch
The seminar covers different topics within the field of representation theory.
Schedule of Talks
 Wednesday, 20 Oct, 10:15
 JanPaul Lerch: The spectrum of $\mathbb R$

No talk on Wednesday, 27 Oct
 Wednesday, 03 Nov, 10:15
 Julia Sauter: Tilting subcategories of exact categories
 Wednesday, 10 Nov, 10:15
 Bill CrawleyBoevey: Deformed preprojective algebras
 Wednesday, 17 Nov, 10:15
 Raphael BennettTennenhaus: Higher AuslanderReiten theory I
 Wednesday, 24 Nov, 10:15
 Abstract: There seems to be no text book which treats SchurWeyl duality in full generality (e.g. over any infinite field). The aim of this talk is to sketch a possible „textbook proof“. The main result is valid for any commutative base ring, and a crucial ingredient is the fact that any Schur algebra is quasihereditary.
 Henning Krause: SchurWeyl duality
 Wednesday, 08 Dec, 10:15
 Abstract: Let $\Bbbk$ be an algebraically closed field, let $\Lambda$ be a finite dimensional $\Bbbk $algebra, and let $\widehat{\Lambda}$ be the repetitive algebra of $\Lambda$. For the stable category of finitely generated left $\widehat{\Lambda}$modules $\widehat{\Lambda} $$\underline{mod}$, we show that the irreducible morphisms fall into three canonical forms: (i) all the component morphisms are split monomorphisms; (ii) all of them are split epimorphisms; (iii) there is exactly one irreducible component. We next use this fact in order to describe the shape of the AuslanderReiten triangles in $\widehat{\Lambda}$$\underline{mod}$. We use the fact (and prove) that every AuslanderReiten triangle in $\widehat{\Lambda}$$\underline{mod}$ is induced from an AuslanderReiten sequence of finitely generated left $\widehat{\Lambda}$modules. Finally, we will talk about applications of this last result.
 Hernán Giraldo (Universidad de Antioquia): Shapes of Auslander Reiten triangles in the stable category of modules over repetitive algebras.

No talk on Wednesday, 12 Jan
 Wednesday, 19 Jan, 10:15
 Raphael BennettTennenhaus: Higher AuslanderReiten theory II
 Wednesday, 26 Jan, 10:15
 Vincent Klinksiek: Auslander Reitentheory for string algebras
 Wednesday, 02 Feb, 10:15
 Abstract: Let $G$ be an extension of a group of odd order by an elementary abelian $2$group of rank $2$. It is known that the total homology of an arbitrary perfect complex over $\mathbb{F}_2[G]$ is either zero or at least fourdimensional. I will report on joint work with Henrik Rüping in which we study perfect complexes with fourdimensional total homology. As an application, I will provide restrictions for the existence of free $A_4$actions on a product of two spheres. This is also joint with Ergün Yalcin.
 Marc Stephan: Perfect complexes with small homology over $\mathbb{F}_2[(\mathbb{Z}/2)^2\rtimes Q]$

Wednesday, 02 Feb, 14:15, room V4116
 Henning Krause: The higher AuslanderReiten formula