I am a number theorist, especially interested in the arithmetic theory of modular forms. One of the central tools I have been using is the theory of modular symbols.
(With Romyar Sharifi, Sheng-Chi Shih and Jun Wang) Eisenstein cocycles for imaginary quadratic fields. Preprint 2025, submitted (arXiv).
(With Jun Wang) On the arithmetic of special values of L-functions for certain abelian varieties with a rational isogeny. Preprint 2023, submitted (arXiv).
On Eisenstein congruences and beyond, Notices of the International Consortium of Chinese Mathematicians, Volume 11, Number 1, pp. 160-183, 2023.
(With Jun Wang) Level compatibility in Sharifi's conjecture. Canadian Mathematical Bulletin, 66(4), pp. 1194-1212, 2023
On triple product L-functions and a conjecture of Harris--Venkatesh. International Mathematics Research Notices, Volume 2023, Issue 22, pp. 19476–19506, 2023.
On the Mazur--Tate conjecture for prime conductor and Mazur's Eisenstein ideal. American Journal of Mathematics, Volume 145, Number 5, pp. 1365-1387, 2023.
Higher Eisenstein elements, higher Eichler formulas and rank of Hecke algebras. Inventiones mathematicae volume 223, pages 485–595 (2021).
Mixed modular symbols and the generalized cuspidal 1-motive. Transactions of the American Mathematical Society, 374 (2021), 2823-2872.
(With Jun Wang) On a conjecture of Sharifi and Mazur's Eisenstein ideal. International Mathematics Research Notices, Volume 2022, Issue 1, January 2022.
(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.
On the Galois structure of the class group of certain Kummer extensions, Journal of the London Mathematical Society, Volume 98, Issue 1, August 2018.
(With Adel Betina) Congruence formulas for Legendre modular polynomials, Journal of Number Theory, Volume 188, July 2018, Pages 71-87.
(With David Zmiaikou) On a conjecture of H. Gupta. Discrete Mathematics, Volume 312, Issue 8, April 2012, Pages 1444-1452.