Research

My research interests are in computational & analytic number theory.  In general, I am interested in any problem that might involve modular forms which are mysterious functions with a lot of symmetry.  I love programming and I love pure math, so one can say I hit the jackpot.

My thesis was on developing techniques for computing a type of modular forms called Bianchi modular forms (modular forms over imaginary quadratic fields) with special properties (non-trivial class groups.)  With the help of my postdoc advisor, I am expanding towards understanding more about classical modular forms and Harmonic Maass forms.

Bianchi Modular Forms stuff: 

Modular forms as they are classically defined are challenging to compute. Brilliant mathematicians like Birch, Manin, Mazur, Merel, and Cremona (and many others) have worked hard to effective ways to compute them. I am trying to see how much of the theory they developed can be used for computing Bianchi Modular Forms over imaginary quadratic fields that have a "bigger" class number.  I implemented an algorithm to compute Bianchi Modular forms over imaginary quadratic fields with higher-class numbers. We are working on the paper right now. In the future, I plan to work on extending my computations to more general number fields and for higher-weight cases. 

Harmonic Maass Forms: 

(coming soon)