- Algebraic Combinatorics, Root Systems, Coxeter systems, Hecke Algebras and their Combinatorics
- Algebraic Groups, Lie Algebras and their Representations, Algebraic Invariant Theory
- Enumerative Geometry on Homogeneous Spaces
- Geometric Representation Theory, Geometry of Flag Manifolds
- Quantum Groups (Quantized Universal Enveloping Algebras and Quantum Function Algebras) and their Representations
- Super Groups, Lie Superalgebras and their Representations
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