Older Papers


A Shintani-Type Formula for Gross-Stark Units over Function Fields (with Samit Dasgupta), Journal of Mathematical Sciences, The University of Tokyo, 16 (2009), no. 3, pages 415-440. (pdf)

Arithmetic traces of non-holomorphic modular invariants (with Aaron Pixton), International Journal of Number Theory, 6 (2010), pages 69-87. (pdf)

Orders at infinity of modular forms with Heegner divisors (with Carl Erickson and Aaron Pixton), Proceedings of the American Mathematical Society 135 (2007), pages 3115-3126. (pdf)

Asymptotic bounds for permutations containing many different patterns, Journal of Combinatorial Theory Series A, 116 (1) (2009), pages 92-108. (ps)

Senior Thesis

Explicit Class Field Theory in Function Fields: Gross-Stark Units and Drinfeld Modules, my senior thesis from Harvard University, 2008. (pdf)
This consists of a proof (under a certain simplifying condition of the formula from my paper with Dasgupta above, preceded by exposition concerning the conjecture (Dasgupta's refinement of Gross's conjecture) that this formula confirms, and concerning the methods (the theory of Drinfeld modules developed by Hayes) that it uses.