Group theory and related topics

My particular interests include the following topics:

(i) Finite group theory:

  • Classification of finite p-groups.

  • Influence of conjugacy class sizes on the structure of finite groups.

  • Automorphisms of p-groups.

  • Camina p-groups.

  • Word maps in groups.

  • Various graphs associated with groups.

(ii) Combinatorial group theory:

  • Coxeter groups and Artin groups: Combinatorial aspects, automorphisms, and rigidity problem.

  • (Planar) braid groups and related structures arising in low dimensional topology.

(iii) Nilpotent Lie algebra:

  • Classification of finite dimensional (nilpotent) Lie algebras.

  • Structure of Camina Lie algebras.

  • Word maps in (nilpotent) Lie algebras.