David Corwin's Old Page

After MIT, I have become a postdoc at UC Berkeley. See my new webpage at Berkeley.

My work always tried to unite the truth with the beautiful, but when I had to choose one or the other, I usually chose the beautiful. - H. Weyl

I have just finished a Ph.D. in mathematics at MIT. I will be a postdoc at U.C. Berkeley starting in Fall, 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 enjoy learning languages, discovering the secrets of the universe (or other universes), and visiting cool places.


Mathematical Writing

My PhD Thesis


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

(Joint with I. Dan-Cohen)

A Generalized Obstruction to Rational Points

(Joint with T. Schlank)

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

(Joint with T. Feng, Z. Li, and S. Trebat-Leder)

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

(Joint with A. Brookner, P. Etingof, and S. Sam)

Slides on Research:

Slides on Explicit Motivic Chabauty-Kim Theory (emphasis on periods)

Slides on Explicit Motivic Chabauty-Kim Theory (emphasis on non-abelian Chabauty)

In preparation:

Cuspidal Sections of Algebraic Fundamental Groups of Higher Dimensional Varieties

Adelic Galois Representations of Abelian Surfaces with Real Multiplication

(Joint with T. Feng, Z. Li, and S. Trebat-Leder)


Galois Groups and Fundamental Groups

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)

Convergence of Fourier Series

Local Class Field Theory Via Galois Cohomology

Proof of the Prime Number Theorem

See here for a blog I used, mostly in high school.

Semi-Original Notes

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

profile for David Corwin at MathOverflow, Q&A for professional mathematicians




Contact Information

Email: corwind@mit.edu

Postal Address:
75 Bertwell Road
Lexington MA 02420