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.
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).