### Character Theory of Finite Groups SS 2019

#### Schedule

Lecture: |
Tuesdays | 10:00 - 11:30 | Room 48-438 | Lecturer: |
Jun.-Prof. Dr. Caroline Lassueur |

Exercises: |
Fridays | 11:45 - 13:15 | Room 48-438 | Assistant: |
Bernhard Böhmler, M.Sc. |

**Public holidays / Exceptional schedule:**

- 14th of May: the lecture will be given by Bernhard Böhmler;
- 11th of June: there is no lecture.

**Office hours**: If you have questions, please feel free to come by our offices whenever you wish.

**Exam Dates:**

- Combination
*Character Theory/Quadratic number fields*(with W. Hart): 13.09.2019, 24.10.2019 - Combination
*Character Theory/Plane Algebraic Curves*(with M. Schulze): 18.09.2019, 24.10.2019

#### Exercises

The exercise classes begin in the 2nd week of the lecture period and then take place every second week. See [KIS] for the precise dates.

The 1st exercise sheet will be uploaded after the 1st lecture. From Sheet 2 on, the exercise sheets will be uploaded on the hand-in day of the previous one.

Exercise Sheet 1. Due date: 25.04.2019, 12:00

Exercise Sheet 2. Due date: 09.05.2019, 12:00

Exercise Sheet 3. Due date: 23.05.2019, 12:00

Exercise Sheet 4. Due date: 06.06.2019, 12:00 (Exercise 16 needs the lecture of the 4th of June)

Exercise Sheet 5. Due date: 21.06.2019, 18:00

Exercise Sheet 6. Due date: 04.07.2019, 10:00

The 1st exercise sheet will be uploaded after the 1st lecture. From Sheet 2 on, the exercise sheets will be uploaded on the hand-in day of the previous one.

Exercise Sheet 1. Due date: 25.04.2019, 12:00

Exercise Sheet 2. Due date: 09.05.2019, 12:00

Exercise Sheet 3. Due date: 23.05.2019, 12:00

Exercise Sheet 4. Due date: 06.06.2019, 12:00 (Exercise 16 needs the lecture of the 4th of June)

Exercise Sheet 5. Due date: 21.06.2019, 18:00

Exercise Sheet 6. Due date: 04.07.2019, 10:00

**Handing in solutions**: Please hand in your solution sheets by Thursdays, noon in the dedicated letter-box next to Lecture Theater 208.**Registration**: Please register for the exercises in the URM system by Thursday, the 18th of April 2019, noon (Holy Thursday).#### Übungsscheine

You obtain an "Übungsschein" if the following criteria are fulfilled:

Each Exercise is worth 4 points.

Exercises can be handed in in groups of maximum two students.

- you have obtained minimum 50% of the points on the Exercise sheets altogether.
- you have obtained minimum 1 point in 2 Exercises (out of 4) in each of the Exercise Sheets 2 to 6.

(1 point on Sheet 1.) - you have actively taken part to the exercise classes: attendance to the exercise classes + presenting at least one solution on the board.

Each Exercise is worth 4 points.

Exercises can be handed in in groups of maximum two students.

#### References

**Textbooks:**

- [JL01] G. James and M. Liebeck,
*Representations and characters of groups.*See [zbMATH]. - [Ser77] J.-P. Serre,
*Linear representations of finite groups*. See [zbMATH].

The original text is:

[Ser98] J.-P. Serre, Représentations linéaires des groupes finis. See [zbMATH]. - [Isa06] M. Isaacs,
*Character theory of finite groups.*See [zbMATH]. - [Web16] P. Webb,
*A course in finite group representation theory*. See [zbMATH]. - [CCNPW85] J.H. Conway, R.T. Curtis, S.P. Norton, R. Parker, R.A. Wilson,
*Atlas of Finite Groups.*Clarendon Press, Oxford, 1985.

#### Oral Exam

In principle one should be able to explain the content of the lecture.

- Definitions, statements of the theorems/propositions/lemmata should be known.
- You should be able to explain short proofs as well as the red lines of the longer proofs.
- The Exercises mentioned in the lecture are important for the understanding of the theory.
- you should also be able to give concrete examples/counter-examples to illustrate the results.
- There will also be questions on concrete examples.
- Also be ready to write down formally the concepts and results you are explaining.