Research

I study analytic number theory, specifically automorphic forms and multiple Dirichlet series. My Ph.D. advisor at Brown University was Jeff Hoffstein.

My thesis deals with GL3 Eisenstein series. I generalize the result of Chinta and Offen in Orthogonal Period of a GL3 Eisenstein Series to the case of the minimal parabolic GL3 Eisenstein series using multiple Dirichlet series associated to the prehomogeneous vector space of ternary quadratic forms. In future work, I plan to generalize further to the maximal parabolic Eisenstein series, and eventually to GL3 Maass forms.

For those interested, here is my research statement, last updated January 2013.

Publications

• The sign of Fourier coefficients of half-integral weight cusp forms, joint with Thomas Hulse, E. Mehmet Kiral, and Chan Ieong Kuan. International Journal of Number Theory, Vol. 08, No. 03, pp. 749-762. We prove that the Fourier coefficients of half-integral weight cusp forms change sign infinitely often. (pdf)
• Multiple Dirichlet Series of Prehomogeneous Vector Spaces and the Relation with GL(3,Z) Eisenstein Series. Brown University Ph.D. thesis.
• Counting Square Discriminants, joint with Thomas Hulse, E. Mehmet Kiral, and Chan Ieong Kuan. Submitted to the Israel Journal of Mathematics. (pdf)

Expository Writings

• The Golden Ratio: All the Cool Stuff Your Mother Never Told You, written November 2012 mainly for knitters who wanted to know more about the golden ratio. (pdf)