My research interests are in computational number theory. I love programming and I love pure math, so one can say I hit the jackpot. I am currently working on my thesis which will be on developing techniques for computing Modular forms over imaginary quadratic fields with non-trivial class groups. Apart from my thesis work, I am working with Tian An Wong and Kim Klinger-Logan continuing our work in the rethinking number theory workshop 2. If you are interested in doing research in number theory, this is a really fun workshop to be a part of.
Modular forms are mysterious function with a lot of symmetry. Also, they are quite hard 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 has a "bigger" class number.
Here are some projects (past and ongoing) I was involved in:
For my master's thesis on Continued fractions with Irrational Denominators with John Greene from Univ. of Minnesota Duluth. You can find my thesis here. This was a really cool project and we got to see a lot of fun patterns of continued fractions.
In this paper, we worked on computing perfect Hermitian forms over Imaginary quadratic number fields for different discriminants to understand how complicated the generalized Voronoi Tessellation gets. You can access the ArXiv preprint here.
I am currently working on finding and implementing an algorithm to compute Bianchi Modular forms over imaginary quadratic fields with higher class number. We are working on the paper right now. In future, I plan to work on extending my computations to more general number fields and for higher weight cases.