Research Interests

I am interested in number theory. My research is motivated by conjectures on special values of L-functions, more precisely, by the Bloch-Kato conjectures. My work is mainly in Iwasawa theory, both classical as well as noncommutative Iwasawa theory. My research is supported by Tata Education and Development Trust.

Publications and preprints

On The Equivariant Tamagawa Number Conjecture. (joint with Samit Dasgupta, Jesse Silliman)
Preprint Link
On the Brumer-Stark Conjecture over Z. (joint with Samit Dasgupta, Jesse Silliman, Jiuya Wang)
Preprint Link
The residually Indistinguishable Case of Ribet's Method for GL_2. (joint with Samit Dasgupta, Jesse Silliman, Jiuya Wang)
Preprint Link
On the Brumer-Stark Conjecture and Refinements. (joint with Samit Dasgupta)
ICM 2022 Proceedings. Link
Brumer-Stark Units and Hilbert's 12th Problem. (joint with Samit Dasgupta)
Accepted for publication in the Duke math journal. Link
On the Brumer-Stark conjecture. (joint with Samit Dasgupta)
Ann. of Math. 197(1) Pages 289-388. Journal Link.
Link
On constant terms of Eisenstein series. (joint with Samit Dasgupta)
Acta Arithmetica. 200 (2021) 119-147. Link
Trivial zeroes in the Iwasawa Main Conjecture. (joint with Samit Dasgupta)
International Colloquium on Arithmetic Geometry, TIFR, to appear.
A note on the main conjecture over Q (joint with Zdzislaw Wojtkowiak).
Osaka J. of Math. 58(1) (2021) 149-170.
Exterior powers in Iwasawa theory (joint with Frauke Bleher, Ted Chinburg, Ralph Greenberg, Romyar Sharifi, Martin Taylor)
Journal of the European Mathematical Society (JEMS). 24(2022), no.3, 967-1005. Link
On Weil-etale cohomology and Artin L-series (joint with David Burns)
Preprint Link
On the rank one Gross-Stark conjecture for quadratic extensions and the Deligne-Ribet q-expansion principle (joint with Samit Dasgupta)
"Adv Studies of Pure Math." (proceedings of Iwasawa 2017) (2020) 243-254 Link
On a refinement of the Birch and Swinnerton-Dyer conjecture in positive characteristic (joint with David Burns and Kim Wansu).
Preprint Link
Unramified Chern-Simons invariants (joint with Frauke Bleher, Ted Chinburg, Ralph Greenberg, George Pappas, Martin Taylor)
New York J. Math. 24 (2018) 514-542.
On the Gross-Stark conjecture (joint with Samit Dasgupta, Kevin Ventullo)
Ann. of Math. 174(1) (2018) 833-870.
Higher Chern classes and Iwasawa theory (joint with Frauke Bleher, Ted Chinburg, Ralph Greenberg, George Pappas, Romyar Sharifi, Martin Taylor)
American J. of Math. 142(2) (2020) 627-682.
Some conjectures for non-CM elliptic curves
in Elliptic curves, modular forms and Iwasawa theory 295-309., Springer Proc. Math. Stat. 2016.
Non-commutative q-expansions
in p-adic aspects of modular forms, 317-331, World Sci. Publ., 2016
On Kato's local $\epsilon$-conjecture: $\ell \neq p$ case
Journal of LMS 90(1), 287-308, (2014)
The main conjecture of Iwasawa theory for totally real fields
Invent. Math. 193(3), 539-626, (2013)
Congruences between abelian p-adic zeta functions
in non-commutative main conjecture for totally real fields, , 125-158, Springer Proc. in Math. Stat., 29, (2013)
From the classical to the non-commutative Iwasawa theory (for totally real number fields)
in Non-abelian fundamental groups and Iwasawa theory, 107-131, London Math. Soc. Lecture Note Ser., 393, Cambridge Univ. Press, (2012)
Proof of the main conjecture of noncommutative Iwasawa theory for totally real number fields in certain cases
J. Algebraic Geometry 20, 631-683, (2011).