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Ph.D., Harvard University (2014)
B.S., Stanford University (2009)
My research centers on algebraic geometry. Algebraic geometry is a very old subject that sits at a nexus between abstract algebra, number theory, complex analysis, and geometry. My own research focuses on using combinatorics to solve problems in algebraic geometry; I am especially excited when I can encode a complicated geometric problem in a simple-to-describe game, and then learn how to win the game.
A favorite topic of mine is the study of chip-firing games on metric graphs. These games are related to the subject of sandpiles in combinatorics, and also have deep and surprising links to algebraic geometry. This subject may be an excellent starting point for students who want to start working on concrete problems right away, and simultaneously gain a window into some of the deeper waters of algebraic geometry.
I teach courses at all levels of the mathematics curriculum. My upper-division courses focus on abstract algebra and its applications, especially subjects related to algorithms and computation. One of my favorite courses is Cryptography, which serves as an introduction to abstract algebra in an applied context, as well as an introduction to programming for mathematics students.
I emphasize problem-solving and intuition in all my courses. I hope to communicate the habits of mind that allow students to both ask and answer challenging questions, rather than simply learning formulas.
Brill–Noether varieties of k-gonal curves. Advances in Mathematics 312 (2017): 46-63.
Special divisors on marked chains of cycles. Journal of Combinatorial Theory, Series A 150 (2017): 182-207.
Genera of Brill-Noether curves and staircase paths in Young tableaux (with M. Chan, A. López Martín, and M. Teixidor i Bigas). To appear in Transactions of the AMS.
Bitangents of tropical plane quartic curves (with M. Baker, Y. Len, R. Morrison, and Q. Ren). Mathematische Zeitschrift 282:3 (2016): 1017-1031.