I am currently looking for a position beginning July 2021. I am now a postdoc at MSRI from August-December 2020 as part of the virtual semester Decidability, definability and computability in number theory, then will finish my postdoc at U.C. Berkeley from January-June 2021. I finished a Ph.D. in mathematics at MIT in 2018.

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

Through Spring 2020, I was a co-organizer of the Berkeley arithmetic geometry and number theory seminar.

Brauer and Etale Homotopy Obstructions on Open Covers (longer version), arXiv preprint.

The polylog quotient and the Goncharov quotient in computational Chabauty-Kim theory I, *International Journal of Number Theory*, 16 (2020), pages 1859-1905.

The polylog quotient and the Goncharov quotient in computational Chabauty-Kim theory II, *Transactions of the American Mathematical Society*, 373 (2020), pages 6835-6861.

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

From Chabauty to Kim (draft) (NEW: Updated September 2020)

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