# Research

## Papers

- A local-global principle for isogenies of composite degree, submitted.
- Interpolation for Brill-Noether curves in P^4, with Eric Larson, preprint.
- Abelian varieties isogenous to a power of an elliptic curve over a Galois extension, submitted.
- Constants in Titchmarsh divisor problems for elliptic curves, with R. Bell, C. Blakestad, A.C. Cojocaru, A. Cowan, N. Jones, V. Matei, and G. Smith, submitted.
- Elliptic fibrations on covers of the elliptic modular surface of level 5, with F. Balastrieri, J. Desjardins, A. Garbagnati, C. Maistret, and C. Salgado, to appear in
*Women in Numbers Europe II*
- Interpolation for Brill-Noether space curves,
*manuscripta mathematica* 156(1), (2018)
- Powers in Lucas sequences via Galois representations, with Jesse Silliman,
*Proc. Amer. Math. Soc.*, 143 (2015)

## Computer Programs

# Conferences I've Organized

# Expository Writing

Polished expository papers and presentations I have prepared which may be of interest:

- The Local Langlands Correspondence for GL_n over a p-adic Field PDF
- Vector Fields on Spheres PDF
- Lefschetz Fixed Point Theorem PDF
- A Brief History of Homotopy Theory (slides from talk for the Harvard History of Math Seminar) PDF

Notes or presentations I have written for my students or myself (some of which are in a very rough form) that may be helpful:

- An Introduction to the Euler Characteristic PDF
- An Introduction to Finite Group Representations with Applications to Chemical Bonding PDF
- DNA Computation (a skeletal presentation covering the work of Adleman and Winfree) PDF .pptx

I have written the Wikipedia article on the Woodward-Hoffmann Rules in physical organic chemistry and molecular orbital theory.
I'd gladly welcome any comments on improving the article.

# Teaching

## Recitation Websites

## Notes and Problems

Here is a presentation I gave on

MIT PRIMES Circle at the

MIT SEPT program in June,
2015:

PDF.

Collected Problems (most written as review problems for my
Math 23 students -- Material may be freely taken from here without credit):

- Linear Algebra Problems:
- Functions, Differential Calculus, Point-Set Topology Problems:

I have prepared materials for a (very brief) Introduction
to LaTeX for math students: PDF .tex