Please put [Lecture Representation theory] as the subject.

- Fourth semester students in Mathematics interested in a mixture of (linear) algebra and discrete mathematics, but everyone is welcome

- The lecture.
- Every Monday from 12:00-14:00
- Online

- Tutorials.
- Every Friday from 12:00-14:00
- Online

- Material for the lecture.
- The lecture is a mix of various sources for group and monoid representations. The main source is [St12] for group representations and then [St16] for the monoid case, and the lecture follows the list of topics presented therein. The lecture sometimes takes a different perspective and potentially reading either of the classical references [CR62], [FH91] or [Se77] should be beneficial. [Be98] is a bit more abstract, but also a classic. Newer references are for example |Cr19], [E+11] (freely available), |Sa01] (for symmetric groups). These are also used for the lecture.
- Prerecorded lectures on the “What is...representation theory?” playlist here: Click

- Summary: Click
- Mini presentation: Click
- The detailed plan: Click

**Speaker**: Daniel Tubbenhauer,**Topic**: The beginnings - What is...representation theory?**Speaker**: Daniel Tubbenhauer,**Topic**: Simple and indecomposable representations I - The elements**Speaker**: Daniel Tubbenhauer,**Topic**: Simple and indecomposable representations II - More about elements**Speaker**: Daniel Tubbenhauer,**Topic**: Characters I - The main players of representation theory!?**Speaker**: Daniel Tubbenhauer,**Topic**: Characters II - Schur's orthogonality relations**Speaker**: Daniel Tubbenhauer,**Topic**: Characters III - Abelian groups and Fourier analysis**Speaker**: Daniel Tubbenhauer,**Topic**: Burnside's theorem - An application**Speaker**: Daniel Tubbenhauer,**Topic**: Induction and restriction - The classical adjoint pair**Speaker**: Daniel Tubbenhauer,**Topic**: Representations of symmetric groups - Young diagrams and co**Speaker**: Daniel Tubbenhauer,**Topic**: Monoids I - Green's relations and friends**Speaker**: Daniel Tubbenhauer,**Topic**: Monoids II - The Clifford-Munn-Ponizovskii theorem**Speaker**: Daniel Tubbenhauer,**Topic**: Whats next? - Outlook

- Exercise 1, Click
- Exercise 2, Click
- Exercise 3, Click
- Exercise 4, Click
- Exercise 5, Click
- Exercise 6, Click
- Exercise 7, Click
- Exercise 8, Click
- Exercise 9, Click
- Exercise 10, Click
- Exercise 11, Click
- Exercise 12, Click

- [Be98] D.J. Benson. Representations and cohomology. I. Basic representation theory of finite groups and associative algebras. Second edition. Cambridge Studies in Advanced Mathematics, 30. Cambridge University Press, Cambridge, 1998. xii+246 pp.
- |Cr19] D.A. Craven. Representation theory of finite groups: a guidebook. Universitext. Springer, Cham, 2019. viii+294 pp.
- [CR62] C.W. Curtis, I. Reiner. Representation theory of finite groups and associative algebras. Reprint of the 1962 original. AMS Chelsea Publishing, Providence, RI, 2006. xiv+689 pp.
- [E+11] P. Etingof, O. Golberg, S. Hensel, T. Liu, A. Schwendner, D. Vaintrob, E. Yudovina. Introduction to representation theory. With historical interludes by Slava Gerovitch. Student Mathematical Library, 59. American Mathematical Society, Providence, RI, 2011. viii+228 pp. https://math.mit.edu/~etingof/replect.pdf
- [FH91] W. Fulton, J. Harris. Representation theory. A first course. Graduate Texts in Mathematics, 129. Readings in Mathematics. Springer-Verlag, \newblock New York, 1991. {\rm xvi}+551 pp.
- |Sa01] B.E. Sagan. The symmetric group. Representations, combinatorial algorithms, and symmetric functions. Second edition. Graduate Texts in Mathematics, 203. Springer-Verlag, New York, 2001. xvi+238 pp.
- [Se77] J.P. Serre. Linear representations of finite groups. Translated from the second French edition by Leonard L. Scott. Graduate Texts in Mathematics, Vol. 42. Springer-Verlag, New York-Heidelberg, 1977. {\rm x}+170 pp.
- [St12] B.Steinberg. Representation theory of finite groups. An introductory approach. Universitext. Springer, New York, 2012. xiv+157 pp.
- [St16] B. Steinberg. Representation theory of finite monoids. Universitext. Springer, Cham, 2016. xxiv+317 pp.