Research

"Primitive Integral Solutions to x^2 + y^3 = z^10," to be submitted.

Using modular methods and Chabauty techniques for elliptic curves over number fields, we classify the primitive integer solutions to x^2 + y^3 = z^{10}

.pdf version
ArXiv version
Transcripts of computations

The Chabauty Coleman Bound at a Prime of Bad Reduction (preprint, slightly revised from the arXiv version)

We extend the sharp version of the Chabauty-Coleman bound on the number of rational points on a curve of genus g > 1 to the case of bad reduction.

(I took this down because I found an error that may not be fixable.)

Expository

Serre Spectral Sequences and Applications (Term Paper for Peter Teichner's Math 215b, Algebraic Topology; May 2, 2006)    

Spectral sequences are a key theoretical and computational tool in algebraic topology. This paper is a tutorial essay, intended for students and researchers as a quick introduction, providing a few nice examples, applications, and a short list of references for further inquiry.

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Lecture Notes

   

My notes	Course title (link to course page)	Lecturer(s)	Semester	Additional Resources
(pdf)	Moduli of Surfaces	BAGS: the joint Harvard/MIT Baby Algebraic geometry seminar	Fall 2007
(pdf)	Finite Groups in Number Theory	Lectures by Serre	Fall 2007