Integral Gassman equivalence of algebraic and hyperbolic manifolds with D.B. Mcreynolds, D. Arapura, and P. Solapurkar (submitted for publication, link to arXiv).

Some expository papers on:

Number theory

Explicit computation of intermediate subfields of cyclotomic extensions–final paper for a course in number theory, based on notes from Paul Garrett.

Zeta functions of real quadratic fields as periods of Eisenstein Series–an extension of an elementary computation of Paul Garrett to the case of nontrivial class number. The ‘better’ way to perform this computation is adelically, which uniformly dispatches all cases–independent of class number and ramification at infinity.

Notes on Tate’s thesis–some (unfinished) notes for a talk I gave in a course on classfield theory.

Groups and their representations

On the isomorphism G/G_x = X–my notes on a writeup by Paul Garrett, proving both a topological and smooth analogue of the classical orbit stabilizer lemma.

Eigenfunction decompositions of function spaces on various physical domains–My undergraduate thesis, under Jerry Shurman, based on notes by Paul Garrett. After setting up some functional analytic machinery and some representation theory of Lie groups, I prove some higher dimensional/non-abelian analogues of the Fourier-decomposition of functions on the circle.

Computer vision

Computer vision poster–A poster summarizing Irena Swanson and my proof of a conjecture by Anders–Hayden, giving an algebraic approximation to the so-called ‘multiview variety.’  This work was funded by the Reed College student research fellowship.

A primary decomposition in computer vision–an (unfinished) paper on the above.