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My research lies at the meeting ground of algebra, number theory and
algebraic geometry. More precisely, I am primarily interested in various
properties of algebraic groups over non-algebraically closed fields, with
special focus on local and global fields. I also study linear representations
of finitely generated groups using the technique of representation varieties
and try to understand the phenomenon of representation rigidity.
Some topics I have worked on are the following:
- Class numbers and class groups of algebraic groups
- Normal subgroup structure of the groups of rational points of algebraic groups over global fields
- Local-global principles
- The congruence subgroup and metaplectic problems for algebraic groups
- Groups with bounded generation and their applications
- Linear representations of finitely generated groups
- Multiplicative structure of finite dimensional division algebras
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