I have just finished a Ph.D. in mathematics at MIT. I am now a postdoc at U.C. Berkeley.

I was previously an undergraduate student in mathematics at Princeton University. Before that, I was a high school student in Acton in Massachusetts.

I am interested primarily in number theory and its relations to algebraic geometry and homotopy theory. I am also interested in representation theory, physics, and logic.

I enjoy learning languages, discovering the secrets of the universe (or other universes), and visiting cool places.

Here is an attempt to collect language exchange opportunities at UC Berkeley.

I am a co-organizer of the Berkeley arithmetic geometry and number theory seminar.

The polylog quotient and the Goncharov quotient in computational Chabauty-Kim theory I

The polylog quotient and the Goncharov quotient in computational Chabauty-Kim theory II

A Generalized Obstruction to Rational Points (longer version)

Elliptic Curves with Full 2-Torsion and Maximal Adelic Galois Representations, *Mathematics of Computation*, 83 (2014), pages 2925-2951.

On Cohen-Macaulayness of S_n-invariant subspace arrangements, *International Mathematics Research Notices*, IMRN 2016, no.7, pages 2104-2126.

Cuspidal Sections of Algebraic Fundamental Groups of Higher Dimensional Varieties

Adelic Galois Representations of Abelian Surfaces with Real Multiplication

Symmetry and the Cubic Formula

Galois Groups and Fundamental Groups (NEW: Updated March 2020)

A Treatise on Elementary Galois Theory

Some Basics on Linear Algebraic Groups Over Algebraically-Closed Fields *(Final paper for a course on algebraic geometry, Fall 2010)*

Systems of l-adic Representations and Elliptic Curves *(Junior Paper, Fall 2011)*

Complex Multiplication *(Junior Paper, Spring 2012)*

Images ouvertes et la conjecture de Manin-Mumford *(Mémoire pour géométrie diophantienne, Paris, Spring 2012)*

Suites spectrales, hypercohomologie, et catégorie dérivée

Model Theory and the Ax-Grothendieck Theorem *(Handwritten notes for a talk, Fall 2012)*

Valuation Spectrum of a Ring *(Handwritten notes for a talk in MIT STAGE, Fall 2013)*

Admissible Representations of p-adic Groups *(Handwritten notes for a talk in the BU Local Langlands learning seminar, Spring 2014)*

Valuation Spectrum of a Ring *(Handwritten notes for a talk in MIT STAGE, Fall 2013)*

Topological aspects of the fundamental group of the projective line minus three points *(Handwritten notes for a talk in MIT STAGE, Fall 2014)*

The de Rham Period Ring I *(Handwritten notes for a talk in BU P-adic Hodge Theory learning seminar, Fall 2014)*

Local Class Field Theory Via Galois Cohomology

Proof of the Prime Number Theorem

See here for a blog I used, mostly in high school.Remarks on the Hodge Filtration in Brown and Kim

A Proof of a Case of Dirichlet's Theorem

Groupe de Mumford-Tate d'une courbe elliptique à τ transcendant

Solution to Putnam 2012 B6 Using Algebraic Number Theory

A Quick Proof that the Character Table is a Square

An Algorithmic Proof of the Nullstellensatz

Image of Inertia on the Tate Module Attached to an Abelian Variety

Permanent Email: last name, then my first initial, then @, then alum, next a period, then mit, then dot edu

Berkeley Email: first initial, then last name, then @, then berkeley, then dot edu

Postal Address:

75 Bertwell Road

Lexington MA 02420

USA