About the Author

I think of Mathematics as a non-linear narrative passed down throughout generations of humankind; mathematicians are the keepers of these stories and their associated problems that have been passed down by their ancestors. From this angle, I am interested in mathematics as a whole. Ive never met a theorem which I disliked but I have seen some theorems which I would call propositions.

My research is Algebraic Number Theory (as initiated by the great Johann Carl Friedrich Gauss). This means I am interested in (1) the solutions of polynomial equations in one or more variables over finite fields and (2) studying the arithmetic invariants associated to algebraic/arithmetic schemes over the algebraic numbers/integers . Most papers in Algebraic Number theory, however, are far removed from this setting. There is a unified way to understand both of these questions: Zeta functions (L-Functions). Reciprocity laws are (these days) represented by proving analytic continuation of the Artin L-functions, associated to nontrivial Galois representations, to the entire complex plane (Langlands Program). Studying arithmetic invariants is understood through the special values, poles, zeros, and residues of the associated L-functions. One amazing example being the Hasse-Weil Zeta function of an elliptic curve defined over the rational numbers (Modularity of Elliptic Curves and the Birch-Swinnerton Dyer Conjecture).

My current research is on mod-p congruences of systems of Hecke-Eigenvalues of genus 2 ordinary Siegel Modular forms with emphasis on proving Level Lowering theorems and computing lower bounds on the degrees of Hida Families via p-adic L-Invariants.