I earned a BS and MS in mathematics from Caltech in 2009, an MA in mathematics from UW-Madison in 2010, and my PhD in mathematics from UW-Madison in 2014.
I am an algebraic number theorist by training. However, my interests also include a number of other topics, such as arithmetic dynamics, algebraic combinatorics, finite-field arithmetic and geometry, elliptic curves and modular forms, competition mathematics, and many other things too numerous to list here.
Past and current projects of mine have involved finite-field hypergeometric functions and Kloosterman sums, arithmetic statistics of number fields, Kakeya sets over non-archimedean local rings, and computational aspects of p-adic modular forms.
Specific Research Interests
Arithmetic statistics of number fields, algebraic Kakeya-type problems over finite fields and local rings, geometry of numbers, overconvergent modular symbols, competition/recreational mathematics.
Courses Offered (subject to change)
- MTH 141 Calculus I
- MTH 171 Honors Calculus I
- Characterizations of Quadratic, Cubic, and Quartic Residue Matrices (with D. Dummit and H. Kisilevsky), submitted (arxiv)
- Explicit Computations of Hida Families via Overconvergent Modular Symbols (with M. Hablicsek, R. Harron, L. Jain, R. Pollack, and D. Ross), submitted (arxiv)
- Counting Number Field Extensions of Given Degree, Bounded Discriminant, and Specified Galois Closure, Ph.D. thesis (pdf).
- Kakeya Sets over Non-Archimedean Local Rings, Mathematika, 2013 (with M. Hablicsek) (arxiv)
- A Conjecture of Evans on Sums of Kloosterman Sums, Proceedings of the American Mathematical Society, 2010 (with A. Goldberg and A. Perry) (pdf)