Research Interests
Broadly speaking, my area of research is Number Theory. I'm specially drawn to questions that lie at the intersection of algebraic number theory, Galois theory, and Galois cohomology.
Here are some of the specific projects I’m currently working on:
- Fontaine-Mazur conjetcure and it's variants: A central theme in my work is exploring which groups can appear as Galois groups of pro-p extensions of number fields with restricted ramification, understanding their structure, behavior, and distribution. These questions are inspired by the work of N. Boston, F. Hajir, C. Maire.
- Witt vectors of associative rings: Classically, given a commutative ring R there is a associated Witt ring W(R), which is an important tool in arithmetic geometry and homotopy theory. There are seemingly different and intriguing constructions of the group of Witt vectors in the non-commutative set up. A natural question is how these constructions are related and is there a universal construction of Witt group functor? This project revolves around the work of J. Cuntz, C. Deninger and L. Hesselholt.
- Arithmetic aspects of locally symmetric spaces: These spacess often arising from arithmetic groups acting on symmetric spaces, encode deep arithmetic information. I am interested in exploring how these spaces reflect properties of algebraic groups over number fields—especially through questions of isospectrality, weak commensurability, and representation equivalence. These questions are inspired by the work of G. Prasad, A. Rapinchuk and C. S. Rajan.
Pre-prints and Published Papers