Short Bio

I was trained in Computational Algebra and Inverse Galois Theory. My thesis focused on computing the locus of genus 2 curves with (n,n)-split Jacobians, a significant computational effort involving Gröbner bases, invariants of group actions, and invariant theory. I computed the cases for n=3, 5 and provided a general method for higher n. These equations were verified for the first time by A. Kumar 15 years later and remain relevant in isogeny-based cryptography and the computation of (n,n)-isogenies.

Along the way, I learned some coding theory, algebraic geometry, and number theory. Some areas of my research are presented below. Click on the items on the right for links to my papers, teaching, editorial work, and other activities. The grouping below loosely categorizes my research and is intended primarily for personal use. If you are interested in collaborative research, please feel free to contact me or complete the form 

Words of Wisdom

"This poor guy is a victim of the system, one of those people who can't write down an equation even if their life depended on it."
— A famous mathematician, speaking about a "modern algebraic geometer".

"Maybe you’ll find yourself in a mediocre department where your work is intentionally undervalued, people with much lesser research records are promoted before you, and hypocrites and frauds run wild. Don’t get discouraged; don’t give up! Remember why you got into math? It wasn’t for the money, recognition, or fame—it was for that special feeling you get when you find the perfect solution or understand a beautiful argument. That hasn’t changed, son! If you still have that magical feeling, you’re doing fine."
– From Dad.

"I can't believe they destroyed a perfectly good old farm to build this damn university."
– From an old colleague.

David Hilbert’s radio address - English translation.

“There is a secret to mathematics: do what you can, not what you dreamed of doing. And try to learn from any paper that you write.”
– John Thompson, after my dissertation defense

“Certainly the best times were when I was alone with mathematics, free of ambition and pretense, and indifferent to the world.” Langlands, in Mathematicians: An Outer View of the Inner World.
-From James Milne website