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.