### YOUNG ALGEBRAISTS' CONFERENCE 2021

EPFL, 6th-10th September 2021

### *Introduction to the Modular Representation Theory of Finite Groups*

#### Preliminary Reading

The following short notes provide a short recap on elementary concepts of module theory, which I will use throughout the lectures.

I assume you should have come across this material in a lecture on Rings and Modules / Commutative Algebra / Algebraic Geometry / ... If it is not the case, do not hesitate to let me know before the start of the school.

I assume you should have come across this material in a lecture on Rings and Modules / Commutative Algebra / Algebraic Geometry / ... If it is not the case, do not hesitate to let me know before the start of the school.

#### Lecture Notes

I have invested some time in producing a pdf version of my blackboard talks containing some general explanations and motivation about each topic treated. A first draft is available here:

You can help me improve them! Please feel free to e-mail me if you find typos or have suggestions for improvements.

If you'd like a handout of my beamer presentations as well, just drop me an e-mail.

You can help me improve them! Please feel free to e-mail me if you find typos or have suggestions for improvements.

If you'd like a handout of my beamer presentations as well, just drop me an e-mail.

#### Exercises

The exercises are to be found in the lecture notes. They are placed precisely where the relevant material to solve them has been presented.

#### References

Fur further reading on the topics treated in this mini-course, I recommend the following textbooks and surveys:

A nice, smooth and complete introduction to representations of finite groups for beginners can be found in Peter Webb's book, which I highly recommend:

**Notes from Summer School Lectures.**- [Bro92] M. Broué,
*Equivalences of blocks of group algebras.*[MathSciNet] - [Kes07] R. Kessar,
*Introducton to block theory.*[MathSciNet] - [Kue18] B. Külshammer,
*Basic local representation theory.*[MathSciNet] - [HKK10] G. Hiss, R. Kessar, B. Külshammer,
*An Introduction to the Representation Theory of Finite Groups*[Unpublished] - [Samb16] B. Sambale,
*Determination of block invariants*[Unpublished]

A nice, smooth and complete introduction to representations of finite groups for beginners can be found in Peter Webb's book, which I highly recommend:

- [Web16] P. Webb,
*A course in finite group representation theory.*[MathSciNet]

**Further Books.**- [Alp86] J. L. Alperin,
*Local representation theory.*[MathSciNet] - [Ben98] D. J. Benson,
*Representations and cohomology I.*[MathSciNet] - [Cra19] D. Craven,
*Representation theory of finite groups: a guidebook*. [MathSciNet] - [CR81] C. Curtis and I. Reiner,
*Methods of representation theory. Vol. I.*[MathSciNet] - [Dor72] L. L. Dornhoff,
*Group representation theory. Part B: Modular representation theory.*[MathSciNet] - [EH18] K. Erdmann and T. Holm,
*Algebras and representation theory.*[MathSciNet] - [Lin18] M. Linckelmann,
*The block theory of finite group algebras. Vol. I and II.*. [MathSciNet] - [LP10] K. Lux and H. Pahlings,
*Representations of Groups, A Computational Approach.*[MathSciNet] - [NT89] H. Nagao and Y. Tsushima,
*Representations of finite groups.*[MathSciNet] - [Nav98] G. Navarro,
*Characters and blocks of finite groups.*[MathSciNet]