Workshop Linear Algebraic Groups

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

  1. Algebraic Groups and basic constructions with algebraic groups
  2. Multiplicative Groups, unipotent groups, solvable groups
  3. Reductive groups, Maximal tori, Borel subgroups, parabolic groups
  4. 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:

  1. Lecture notes by Torsten Wedhorn on basic theory of algebraic groups
  2. Lecture notes by Torsten Wedhorn on structure theory of algebraic groups and representations (fairy tales and basics)
  3. 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)
  4. Lecture notes of Annika Jäger on homogeneous spaces.
  5. Lecture notes by Torsten Wedhorn on  quotients of algebraic groups
  6. Lecture notes by Catrin Mair on diagonalizable groups.
  7. Lecture notes by Jacob Burgi on unipotent groups.
  8. Lecture notes by Torsten Wedhorn on solvable groups.
  9. Lecture notes by Christopher Lang on separated and proper morphisms.
  10. Lecture notes by Lena Volk on Borel’s Fixed Point Theorem
  11. Lecture Notes by Torsten Wedhorn: Summary on resolvable groups
  12. Lecture Notes by Can Yaylali on maximal tori, parabolic subgroups, Borelsubgroups
  13. Lecture Notes by Torsten Wedhorn on Reductive and semisimple groups
  14. Lecture Notes by Till Rampe on root data. 
  15. Lecture notes by Torsten Wedhorn on Classification of reductive groups
  16. Supplement: Example of the symplectic group

Some questions

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