I am a number theorist, especially interested in the theory of modular forms. One of the central tools I have been using is the theory of modular symbols. 

Here is a list of specific subjects I have been working on (roughly sorted from least to most recent).

• Eisenstein ideals, following the work of Mazur.

• Classical algebraic number theory, in particular K-groups of rings of integers.

• Galois representations and their deformations.

• p-adic uniformization of Shimura curves.

• The theory of 1-motives, developed by Deligne.

• Bianchi 3-manifolds, and their relation with arithmetic.

• The BSD conjecture and its variants, in particular the "refined" conjectures of Mazur and Tate.

• Cohomology arithmetic groups and derived Hecke operators.

Publications and Preprints

1. (With Jun Wang) On the Birch and Swinnerton-Dyer conjecture for certain abelian varieties with a rational isogeny. arXiv 

2. (With Jun Wang) Level compatibility in Sharifi's conjecture. arXiv Accepted in Canadian Mathematical Bulletin.

3. On triple product L-functions and a conjecture of Harris--Venkatesh. arXiv Accepted in International Mathematics Research Notices.

4. On the Mazur--Tate conjecture for prime conductor and Mazur's Eisenstein ideal. Accepted in American Journal of Mathematics. Video.

5. Higher Eisenstein elements, higher Eichler formulas and rank of Hecke algebras. Inventiones mathematicae volume 223, pages 485–595 (2021). Full-text available here. Video.

6. Mixed modular symbols and the generalized cuspidal 1-motive. Transactions of the American Mathematical Society, 374 (2021), 2823-2872.

7. (With Jun Wang) On a conjecture of Sharifi and Mazur's Eisenstein ideal.  International Mathematics Research Notices, Volume 2022, Issue 1, January 2022.

8. (With Adel Betina) On the p-adic periods of the modular curve X(Γ0(p) ∩ Γ(2)),  Transactions of the American Mathematical Society, Volume 371, Number 1, 1 January 2019, Pages 413–429.

9. On the Galois structure of the class group of certain Kummer extensions, Journal of the London Mathematical Society, Volume 98, Issue 1, August 2018.

10. (With Adel Betina) Congruence formulas for Legendre modular polynomials, Journal of Number Theory, Volume 188, July 2018, Pages 71-87.

11. (With David Zmiaikou) On a conjecture of H. Gupta. Discrete Mathematics, Volume 312, Issue 8, April 2012, Pages 1444-1452.