*Here are the main themes our group is currently working on.*

## Representation theory

- Representations of Coxeter groups and Hecke algebras, basic sets and decomposition matrices
- Representations of Lie algebras and quantum groups, canonical and crystal bases
- Kazhdan-Lusztig theory and Kazhdan-Lusztig cells
- Theory of noncommutative invariants
- Hopf algebras cohomology and group algebras

## Algebraic combinatorics

- Representations theory and conditionned random walks
- Harmonic functions on graphs
- Counting paths in lattices
- Preorder and associated graphs
- Additive number theory and generalisations