Research
I study analytic number theory, specifically automorphic forms and multiple Dirichlet series. My advisor is 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.
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. In preparation.
- Counting Square Discriminants, joint with Thomas Hulse, E. Mehmet Kiral, Chan Ieong Kuan, and Min Lee. In preparation.
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)