Research Interests

Broadly speaking, my area of research is Number Theory. I'm especially 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 conjecture and its variants: exploring which groups can appear as Galois groups of pro-p extensions of number fields with restricted ramification, and understanding their structure, behavior, and distribution. These questions are inspired by the work of N. Boston, F. Hajir, and C. Maire.
Witt vectors of associative rings: classically, given a commutative ring R there is an associated Witt ring W(R), an important tool in arithmetic geometry and homotopy theory. There are intriguing constructions of the group of Witt vectors in the non-commutative setting. A natural question is how these constructions are related and whether there is a universal construction of the Witt group functor. This project is related to work of J. Cuntz, C. Deninger, and L. Hesselholt.
Arithmetic aspects of locally symmetric spaces: these spaces, often arising from arithmetic groups acting on symmetric spaces, encode deep arithmetic information. I’m interested in how these spaces reflect properties of algebraic groups over number fields—especially through questions of isospectrality, weak commensurability, and representation equivalence. This thread is inspired by the work of G. Prasad, A. Rapinchuk, and C. S. Rajan.

Pre-prints and Published Papers

Deficiency of the p-class tower group of a biquadratic number field
In preparation (2025)
Power integral bases in polynomial compositions
(with A. Choudhary and P. Yadav) Submitted (2025)
A universal group-theoretic characterisation of p-typical Witt vectors of non-commutative rings
(with Biswanath Samanta) Pre-print (2025)
A universal group-theoretic characterisation of p-typical Witt vectors
(with Biswanath Samanta) J. Algebra 677, 1–12 (2025)
Towards the Fontaine–Mazur conjecture for bi-quadratic extensions — an example
(with Ramla Abdellatif) J. Number Theory 279, 457–478 (2026). Published online.
From Fontaine–Mazur conjecture to analytic pro-p groups — Survey
(with Ramla Abdellatif, Marine Rougnant, Lara Thomas)
Assoc. Women Math. Ser., 33, Springer, Cham, 1–24 (2024)
Morphisms between two constructions of Witt vectors of non-commutative rings
Proc. Amer. Math. Soc. 148, no. 7 (2020)
On the comparison of two constructions of Witt vectors of non-commutative rings
(with Amit Hogadi) J. Algebra 506 (2018)
On the splitting fields of generic elements in Zariski dense subgroups
(with C. S. Rajan) J. Algebra 457 (2016)
On uniform lattices in real semisimple groups
(with C. Bhagwat) Proc. Amer. Math. Soc. 144, no. 7 (2016)
Commensurability and representation equivalent arithmetic lattices
(with C. Bhagwat and C. S. Rajan) Int. Math. Res. Not. IMRN 8 (2014)
Remark on equi-characteristic analogue of Hesselholt's conjecture
(with Amit Hogadi) Acta Arithmetica 158(2) (2013)
On cohomology of ring of Witt vectors of \( p \)-adic integers
(with Amit Hogadi) J. Number Theory 10 (2011)
Absolute norms of \( p \)-primary units
Journal de Théorie des Nombres de Bordeaux 21 (2009)
The Chow group of zero-cycles on certain Châtelet surfaces
Indag. Math. 19 (2008)
Thesis (2010)