My research is in algebraic number theory and arithmetic geometry. I use methods from modular forms and Galois deformation theory to study special values of L-functions and Iwasawa theory. I enjoy problems that have a computational aspect, or where patterns or new phenomena can be discovered through examples.

The picture above is taken from one of my favourite papers, "Modular Curves and the Eisenstein ideal" by Barry Mazur.

Iwasawa invariants in residually reducible Hida families.

Joint with Rob Pollack. Preprint (2024).

Explicit non-Gorenstein R=T via rank bounds II: computational aspects.

Joint with Catherine Hsu and Carl Wang-Erickson. Research in Number Theory (2023) (ANTS-XV volume). Journal version.

Explicit non-Gorenstein R=T via rank bounds I: deformation theory.

Joint with Catherine Hsu and Carl Wang-Erickson. Preprint (2022).

Another look at rational torsion of modular Jacobians.

Joint with Kenneth A. Ribet. Proceedings of the National Academy of Sciences (2022). Journal version.

A modular construction of unramified p-extensions of Q(N1/p).

Joint with Jaclyn Lang. Proceedings of the American Mathematical Society (2022). Journal version.

The Eisenstein ideal for weight k and a Bloch-Kato conjecture for tame families.

Journal of the European Mathematical Society (JEMS) (2022). Journal version.

Generalized Bockstein maps and Massey products.

Joint with Yeuk Hay Joshua Lam, Yuan Liu, Romyar Sharifi, and Jiuya Wang. Forum of Mathematics, Sigma (2023). Journal version.

The Eisenstein ideal with squarefree level.

Joint with Carl Wang-Erickson. Advances in Mathematics (2021). Journal version. 

The rank of Mazur's Eisenstein ideal.

Joint with Carl Wang-Erickson. Duke Mathematical Journal (2020). Journal version.

Video lecture from an IAS workshop.

Deformation conditions for pseudorepresentations.

Joint with Carl Wang-Erickson. Forum of Mathematics, Sigma (2019). Journal version.

Primitive elements in p-divisible groups.

Joint with Robert Kottwitz. Research in Number Theory (2017). Journal version.

Ordinary pseudorepresentations and modular forms.

Joint with Carl Wang-Erickson. Proceedings of the American Mathematical Society (2017). Journal version.

Video lecture from a workshop at BIRS in Banff, Alberta.

Full level structures revisited: pairs of roots of unity.

Journal of Number Theory (2016). Journal version.

Pseudo-modularity and Iwasawa theory.

Joint with Carl Wang-Erickson. American Journal of Mathematics (2018). Journal version.

Eisenstein Hecke algebras and conjectures in Iwasawa theory.

Algebra and Number Theory (2015). Journal version.

Hecke algebras associated to Λ-adic modular forms.

Journal für die Reine und Angewandte Mathematik (Crelle's Journal) (2015). Journal version.

Expository writing

Taylor-Wiles method for GL(1) in the general case.

Notes for my Arbeitsgemeinschaft talk (2021).