Mathematical Institute of the University of Bonn

Jan Schröer

Teaching WS 20/21

• Master: V4A3 Representation Theory I
  Mi 10.15-11:45, Fr 8:15 - 9:45 (via Zoom)
  Exercise classes: See Webpage of Dr. Gustavo Jasso.
  
  The communication runs mainly via eCampus and via Gustavo Jasso's webpage.
  
  Prerequisites: You need to know some foundations of representation theory of algebras (Krull-Remak-Schmidt, Jordan-Hölder, categories and functors, quivers and path algebras, semisimple algebras, semisimple modules, Jacobson radical, projective modules). In SS 20 I gave an introductory course on representation theory. The lectures notes of this course are now available on eCampus and on Dr. Jasso's webpage (for getting the necessary login data, please Email Dr. Jasso). You should read these notes before the start of WS 20/21. For the first half of RT I you can focus in Parts 1 and 2 of the notes. With the exception of Part 5, the other parts will be needed in the second half.
  
  Content of Representation Theory I: This course is on the representation theory of finite-dimensional K-algebras (associative with 1, mostly non-commutative, K is a field). Of special interest are path algebras of quivers. Here is a list of topics:
  • Introduction to Homological Algebra
  • Reminder on finite-dimensional algebras, path algebras of quivers, properties of finite length modules, semisimple modules, projective modules.
  • Homological dimensions
  • Homological conjectures
  • Morita-Tachikawa correspondence, Auslander correspondence
  
  Lecture notes: There will be complete and very detailed lecture notes. Usually I will upload these notes just before a lecture or immediately after.
  
  Format of the course: All lectures will be via Zoom. I will mostly try to write on my notepad. However, in contrast to a traditional black board lecture, I'm much slower when I use the notepad. So from time to time I might just sketch a lengthy proof, explain all the main steps and key ideas and provide a more detailed proof in the lecture notes. The same applies occasionally to the discussion of lengthy excamples. There will be additional question and answer sessions during the semester. This depends on the demand. I'm also happy to make additional individual or small group Zoom appointments if you have any questions. You can also ask me questions on the lecture notes from the previous semester.
  
  What I expect of you:
  • Please keep your webcam switched on during all Zoom lectures. This will help you concentrate on the lectures and it also creates a much better atmosphere.
  • I expect and encourage that you ask questions during the lecture.
  • I expect that you read the lecture notes on a regular basis.
  • I expect that you actively participate in the Exercise classes.
  
  
  Exams
  1st try: 19.02.2021
  Klausureinsicht: tba.
  
  2nd try: 19.03.2021
  Klausureinsicht: tba.


• Bachelor: S2A1 Hauptseminar Algebra zum Thema Darstellungstheorie von Köchern und Algebren
  Fr 10:15-11:45 (via Zoom)
  Voraussetzungen: Grundlegende Kenntnisse der Darstellungstheorie von Algebren, welche in etwa dem Inhalt meiner derzeitigen Vorlesung entsprechen. Es gibt noch freie Plätze. Bitte melden Sie sich bei mir via Email, falls Sie Interesse haben.
1. 30.10.20
2. 06.11.20
3. 13.11.20
4. 20.11.20
5. 27.11.20
6. 11.12.20
7. 08.01.21
8. 15.01.21
9. 22.01.21
10. 29.01.21
11. 05.02.21