I am a mathematician, having completed my PhD in 2012 at Stanford University. Currently, I am the director of Euler Circle, a mathematics institute for advanced high-school students in Palo Alto, California.
My research interests are broad, including number theory, combinatorics, probability, and game theory.
I love learning new things and working on new research projects. If you would like to do some mathematics with me, I can be easily tempted!
Controlling Ramification in Number Fields
Advisor: Akshay Venkatesh
Papers and preprints
(Links are to arXiv or other free versions.)
- Preprint: Finite ramification for preimage fields of postcritically finite morphisms. With Andrew Bridy, Patrick Ingram, Rafe Jones, Jamie Juul, Alon Levy, Michelle Manes, and Joseph Silverman.
- Preprint: Noncrossing partitions, toggles, and homomesies. With David Einstein, Miriam Farber, Emily Gunawan, Michael Joseph, Matthew Macauley, and James Propp.
- Preprint: Global Fibonacci Nim. With Urban Larsson.
- Preprint: Curvature and Concentration of Hamiltonian Monte Carlo in High Dimensions. With Susan Holmes and Christof Seiler.
- N-Division Points of Hypocycloids. To appear in Arnold Mathematical Journal. With Nitya Mani.
- Grundy values of Fibonacci nim. To appear in International Journal of Game Theory. With Urban Larsson.
- Identities for field extensions generalizing the Ohno-Nakagawa relations. To appear in Compositio Mathematica With Henri Cohen and Frank Thorne.
- Positive Curvature and Hamiltonian Monte Carlo in Advances in Neural Information Processing Systems, 2014. With Susan Holmes and Christof Seiler.
- Analysis on Surreal Numbers in Journal of Logic and Analysis, 2014. With Ashvin Swaminathan.
- Period computations for covers of elliptic curves in Mathematics of Computation, 2014.
- Invariants for A4 fields and the Cohen-Lenstra heuristics in International Journal of Number Theory, 2014.
- Covers of elliptic curves with unique, totally ramified branch points in Mathematische Nachrichten, 2013.
- A Hilbert space approach to bounded analytic interpolation in Complex Analysis and Operator Theory, 2007. With Jeffrey Danciger
Here are a bunch of expository notes I have written over the years.
Here are some of the educational programs I have been involved with recently:
As you probably guessed from the picture, I'm also a cellist. Other hobbies of mine include chess and calligraphy.