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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