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!

**PhD Thesis**

Controlling Ramification in Number Fields

Advisor: Akshay Venkatesh

**Papers and preprints**

- 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 A
_{4}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

**Expository writings**

Here are a bunch of expository notes I have written over the years.

- Existence and uniqueness of Haar measure
- Finitistic dimensions of monomial algebras

This is essentially my undergraduate senior thesis, with only very minor modifications. - The Mathieu Groups
- Differential Posets
- Notes on the shape of the RSK algorithm in combinatorics

**Educational programs**

- Education Program for Gifted Youth
- Julia Robinson Mathematics Festival
- San Jose Math Circle
- Stanford Math Circle
- Stanford Splash
- Stanford Undergraduate Research Institute in Mathematics
- Stanford University Mathematics Camp

**Other stuff**