A summary of my research at the Cornell SPUR program, working on derived algebraic geometry under the guidance of Harrison Chen, with Lin An and Felipe Castellano-Macias.
My senior thesis on the structure of Faltings' proof of the Mordell conjecture and other conjectures (for which Faltings won a Fields Medal), supervised by Martin Olsson.
Final project for my graduate number theory class, in which I managed to sneak in some algebraic geometry. Basically, the Riemann hypothesis has a function field analogue, which translates into a problem about zeta functions of curves over finite fields. This problem was solved by Weil in the 1940s, and remains the strongest piece of evidence we have for the veracity of the Riemann hypothesis. I explain the problem and give a full solution, somewhat simpler than Weil's original, by using the Hodge index theorem. The statements for curves was generalized to statements for algebraic varieties; these are the famous Weil conjectures which were proved by many mathematicians and completed by Deligne in the 70s.
I am very passionate about Hindustani classical music, and I play the harmonium and sitar. I have performed in over 50 concerts around the Bay Area, Los Angeles, and also in Colorado, Oklahoma, and India.