## Research Interests

My research is mainly in Lie Theory and
Representation Theory. In particular,
I am interested in the following topics:

- Lie (color) algebras

- Finite p-groups and associated Lie algebras

- Sporadic simple groups and simple Lie algebras in small characteristics

- Classification of solvable Lie algebras

- Lie coalgebras and Lie comodules

- Lie bialgebras and Lie bimodules

- Lie bialgebras and the classical Yang-Baxter equation

- Leibniz algebras and Leibniz (co)homology

- Hochschild (co)homology

- Cyclic (co)homology

- Quantum groups at roots of unity

- Small quantum groups

- Hopf algebras and the quantum Yang-Baxter equation

- Hopf algebras and tensor categories

- Frobenius algebras

- Clifford algebras

- Hecke algebras

- Cherednik algebras

- Symplectic reflection algebras

- Poisson algebras

- Poisson (co)homology

- Algebraic K-theory

- Invariant theory

- Non-associative algebraic structures

- Classification of algebras in low dimensions

- Power sums and related functions

- Plane algebraic curves

- Geometry and kinematics of planar mechanisms

- Mathematical foundations of quantum physics

- Statistical physics