Department of Computer Science

Bucknell University

Department of Computer Science

335 Dana Engineering Building

Lewisburg, PA 17837

Office: 311 Dana Engineering Building

Office Phone: 570-577-1276

Email:

Here is my Curriculum Vitae.

I do most of my research in the areas of arithmetic geometry and arithmetic dynamics, although I like to dabble in various other subjects. My graduate adviser was Michael Zieve.

- Cryptographic applications of capacity theory: On the optimality of Coppersmith's method for univariate polynomials, with T. Chinburg, B. Hemenway, N. Heninger,
*accepted*, Asiacrypt - On the number of rich lines in high dimensional real vector spaces, with M. Hablicsek,
*Discrete and Computational Geometry*, 55 (2016), no. 4, 955-962 - Separated Belyi Maps, with M. Zieve,
*Mathematical Research Letters*, 21 (2014), no. 6, 1389-1406. - Uniform Boundedness of S-units in Arithmetic Dynamics, with A. Levin, H. Kreiger, T. J. Tucker, Y. Yasufuku, M. Zieve,
*Pacific Journal of Mathematics*, 274 (2015), no. 1, 97-106. - Abelian Surfaces with Prescribed Groups over Finite Fields, with C. David, D. Garton, A. Shankur, E. Smith, L. Thompson,
*Bulletin of the London Mathematical Society*, 46-4 (2014), 779-792. - Some Planar Monomials in Characteristic 2, with M. Zieve,
*Annals of Combinatorics*, 18-4 (2014), 723-729. - Chebyshev mappings of finite fields, with M. Zieve, J. Rosen, B. Weiss,
*Athematical Monthly*, 119-2 (2012), 151-155. - Polynomial Pell Equations,
*in preparation*. - One Parameter Families of Polynomials Splitting Infinitely Often, with M. Satriano, M. Zieve,
*in preparation*.

In addition to research, I also enjoy writing expository papers on interesting mathematics I've thought about. Unless otherwise noted all of these papers should be accessible to advanced undergraduates and above. These papers are for fun, and should not be considered as research mathematics.

- On Additive Polynomials. This paper classifies which polynomials satisfy f(a+b)=f(a)+f(b) for all a and b.
- The Real Topology of Rational Points on Elliptic Curves. As the title suggests, this paper dicusses the topology of the subgroup of rational points on an elliptic curve.

More to come!

Previously at Penn I've taught:

While at Michigan I've taught:

- Math 105 (Precalc), Fall 2008
- Math 115 (Calc 1), Winter 2009
- Math 115 (Calc 1), Fall 2010
- Math 116 (Calc 2), Winter 2011
- Math 385 (Math For Elementary School Teachers), Fall 2012

See what my kids are saying about me!

In my free time I enjoy playing bridge. In the summer of 2009, four Michigan students and I won the Grand National Teams in flight C. You can read about it here. In the summer of 2012, my team and I won the 0-1500 Spingold National Teams event. You can read about our win here

Before getting serious about bridge, I bowled for my high school and college teams, and played classical double bass (although I still dabble in bluegrass, rock, jazz and klezmer).

I was also a counselor at the Ross Program for a number of years. This is a wonderful experience for high schoolers to come and learn about the theory of numbers through experimentation, conjecture and proof.