# Research Interests

My area of research (broadly speaking) is Number theory. Following are my specific interests:

- Local fields, Galois groups and Galois cohomology

- Ring of Witt vectors of an associative rings ( based on the work of Lars Hesselholt)

- Arithmetic aspects of locally symmetric spaces ( based on the work of Gopal Prasad and Andrei Rapinchuk)

## Pre-prints and Published papers

- Comparing two constructions of Witt vectors for small length Witt vectors of associative rings

(in preparation with Biswanath Samanta) - Towards Fonatine-Mazur conjecture for biquadratic extensions - an example

(with Ramla Abdellatif) Submitted (2022) - From Fontaine Mazur conejcture to analytic pro-p groups- Survey

(with Ramla Abdellatif, Marine Rougnant, Lara Thomas)*To appear in Proceedings of Women in Numbers - Europe episode-4*(2022) - 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 on cohomology of Witt vectors

(with Amit Hogadi)*Acta Arithmetica.***158****(2)**(2013) - On cohomology of ring of Witt vectors
of $p$-adic integers and a conjecture of Hesselholt

(with Amit Hogadi)*J. Number Theory***10**(2011) - Absolute norms of p-primary units

*Journal de Theorie des Nombres de Bordeaux*.**21**(2009) - The Chow group of zero-cycles on certain Chatelet
surfaces over local fields.

*Indag. Math.***19**(2008) - Thesis(2010)