# Suitable Topics for Student Projects:

- Work out explicitely the Nichols algebras for A4 (rank 1) and then for the rack T (rank 2).
- Work out and decompose the Deligne-Lusztig characters (both ways) for the groups PSL2(4)=PSL2(5)=A5
- Determine new liftings for certain Nichols algebras from known diagonal liftings, and hence some new pointed Hopf algebras.
- (*) Attempt the techniques by Heckenberger/Vendramin to determine (and maybe classify) finite-dimensional Nichols algebra over rank 2 racks (instead of groups)
- (*) Work out an example of a logarithmic conformal quantum field theory of rank 2 using screening charges.

# Archive

- Lecture "Funktionentheorie"
**SS 2017**. Standard lecture in complex analysis for Bachelor. Topics are complex differentiability, contour integration, Cauchy integral formula, power series expansion, outlook on Riemann surfaces. - Seminar: Root Systems and Lie Algebras Topics are the classification of finite root systems, Weyl groups, semisimple Lie algebras, highest weight modules.
- Seminar Finite Groups And Their Representations
**WS 2014/15**Introduction to the theory of groups and basic representation theory. The main part of the seminar is on character theory. Special emphasis is put on Lie groups over finite fields. - Diploma-Thesis "Game-Theory of the Stock Market", Lisa Kraus,
**7.12.2011**. The influence of mutual ownership to the matrix of a given game shall be analysed with methods from statistical physics and an isomorphy to variations of the Ising model proven (especially we observe a phase transition for high connectivity). - Course "Finite Groups and their Nichols algebras",
**SS 2011**. An introduction to current research and examples in the classification of Nichols algebras with emphasis on groups theory (no Hopf algebra background necessary). - Seminar "Game theory with many players",
**WS 2010/11**. We treat applications of the techniques in statistical physics to game theory in the limit of many players. - Diploma-Thesis "Anyonenmodels from Hopf algebras aus Hopf Algebren", Karolina Vocke,
**24.12.2010**. Work-Out of explicit formulae for characters and fusion rules for the twisted group double (a quasi-Hopf algebra) by introducing projective Yetter-Drinfel'd modules (in the sense of non-proper action) - Course "Hopf Algebras Generating Fusion Rings And Topological Invariants",
**SS 2010**. A basic introduction to Hopf algebras with a strong emphasis to theoretical physics. Climax is the construction of the Dijkgraaf-Witten-Topological Field Theories. Incl. Lecture Notes.