In this workshop we will learn in condensed form about linear algebraic groups over an algebraically closed field. Topics include:

- Algebraic Groups and basic constructions with algebraic groups
- Multiplicative Groups, unipotent groups, solvable groups
- Reductive groups, Maximal tori, Borel subgroups, parabolic groups
- Classification of reductive groups via based root data

**Organizer**

Anton Güthge, Torsten Wedhorn

**Date**September 27 – October 8 in 2021

**Time**

1st week, Monday – Thursday: 8:45 – 11:45

2nd week, Monday – Wednesday: 8:45 – 11:45

There will be additional optional, tutorium-style meetings in the afternoon at 13:30 with the possibility to discuss the material presented that day. If you are doing a talk yourself, you can also use this opportunity to ask questions about it. Details will be given during the workshop.

**Program**

Here you find the program. Some of the talks will be given by the organizer. In addition there are 8 talks that should be given by the participants (marked boldface in the program).

There will be optional sessions in the afternoon: From 13:45, you can join the Zoom meeting to ask any questions you might have about your own upcoming talk. From 14:30, there will be a general, tutorium-like discussion of the material presented that day.

If you are interested to give a talk, please contact Anton Güthge until September 12.

**Zoom coordinates**

All talks will be online via Zoom. Coordinates:

https://tu-darmstadt.zoom.us/j/85771568177?pwd=M3F1Z2NTNmwzLzBhZ0ZFTWI0dEJsQT09

Meeting-ID: 857 7156 8177

Kenncode: 349359

If you have any questions, do not hesitate to contact one of the organizers.

**Lecture notes**

For all lectures there are notes that are linked below:

- Lecture notes by Torsten Wedhorn on basic theory of algebraic groups
- Lecture notes by Torsten Wedhorn on structure theory of algebraic groups and representations (fairy tales and basics)
- Lecture notes by Manuel Hoff on group actions. There are two versions:

– General version about group actions (using notion of flatness)

– Group actions for smooth groups (more elementary) - Lecture notes of Annika Jäger on homogeneous spaces.
- Lecture notes by Torsten Wedhorn on quotients of algebraic groups
- Lecture notes by Catrin Mair on diagonalizable groups.
- Lecture notes by Jacob Burgi on unipotent groups.
- Lecture notes by Torsten Wedhorn on solvable groups.
- Lecture notes by Christopher Lang on separated and proper morphisms.
- Lecture notes by Lena Volk on Borel’s Fixed Point Theorem
- Lecture Notes by Torsten Wedhorn: Summary on resolvable groups
- Lecture Notes by Can Yaylali on maximal tori, parabolic subgroups, Borelsubgroups
- Lecture Notes by Torsten Wedhorn on Reductive and semisimple groups
- Lecture Notes by Till Rampe on root data.
- Lecture notes by Torsten Wedhorn on Classification of reductive groups
- Supplement: Example of the symplectic group

**Some questions**

Here you find some questions pertaining to separated and proper morphisms.