# Papers

*Note: the papers below should not be taken as an indication of my current research interests, as they all date back to undergraduate research projects. Nevertheless, I welcome fedback regarding any of them. *

## Research 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 Combinatorics Series A, 116 (1) (2009), pages 92-108. (ps)

## Expository Papers

*coming in the future! *

## 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.