My research is in algebra, with primary focus on group rings, unit groups, finite group theory, and representation theory. I am interested in problems where the structure of a finite group is reflected in the arithmetic and algebraic properties of its group rings.

A central theme of my work is the study of unit groups of group rings and related structural questions. In particular, I have worked on the normal complement problem in group algebras, its variants over fields of positive characteristic, and unit groups of group rings over rings such as the ring of integers modulo n.

I am also interested in character-theoretic and computational aspects of finite groups, including Wedderburn decompositions of semisimple group algebras, cut groups and related variants, and classification problems supported by computational algebra.

Group rings and unit groups :

I study the structure of group rings and their unit groups, especially over finite commutative rings and fields. A recurring theme is to understand how the structure of a finite group (G) influences the algebraic properties of the group ring (RG) and its group of units.

Normal complement problem :

Part of my work concerns the normal complement problem in group algebras. This includes studying when certain group-theoretic normal complement properties can be detected from the unit group of a group algebra.

Semisimple group algebras and Wedderburn decompositions :

I am interested in the decomposition of semisimple group algebras and its relation with the representation theory of finite groups. This includes questions involving simple components, character fields, and computational methods.

Character theory and finite groups :

My current interests include character-field restrictions on finite groups, rationality-type conditions, cut groups, and related variants over number fields. I am particularly interested in how such conditions interact with conjugacy, Sylow subgroups, Frobenius groups, and metacyclic groups.

Computational algebra :

I use computational algebra systems, especially GAP, to explore examples, and support classification problems in finite group theory and group rings.