Research Interests:

Algebraic Geometry: Moduli of curves, Moduli of weighted stable maps,

Gromov-Witten Theory, Gravitational Descendants, Intersection Theory

Publications:

5.	Moduli of weighted stable maps and their gravitational
	descendants, dissertation (2007). (directed by V. Alexeev)

4.	Moduli of weighted stable maps and their gravitational
	descendants, math.AG/0607683. (with V. Alexeev. Accepted by
	J. Inst. Math. Jussieu.)

3.	Appendix in: A. Granville and G. Martin. Prime number races
	American Mathematical Monthly and La Gaceta de le Real
	Sociedad Matematica Espanola vol 8.1 (2005) pages 197-240.

2.	Varieties of nilpotent elements for simple Lie algebras II: Bad
	Primes (with UGA VIGRE Algebra Group), J. Algebra 292 (2005),
	65-99.

1.	Varieties of nilpotent elements for simple Lie algebras I: Good
	Primes (with UGA VIGRE Algebra Group), J. Algebra 280 (2004),
	719-737.

Here are some other projects I have worked on:

The Dihedral Group -- This is a project Bree Ettinger and I completed during a summer program on Mathematical Graphics. It is a Java based, animated demonstration of the action of the dihedral group on polygons. If you would like to learn more about what we did there, you may find out more at the program's homepage. Here are some projects that other participants completed! During the 2001 academic year, I worked with Andrew Granville and other students to investigate Prime Number Races related to twin primes. During this work, I wrote a program in C++ to locate and count prime pairs and to track various statistics of the counts in "real time." There is an appendix in math.NT/0408319 (see also the citation for the final publication in item 3. in the list above) which I wrote describing some of our findings. During the Fall of 2003, I worked with with Dave Benson, Brian Boe, Lenny Chastkofsky, and Dan Nakano and other students on a research project studying Varieties of Nilpotent Elements for Semisimple Lie Algebras. During this time we published two papers--citations of these can be found on my CV and on the above list. More information about the group with which I worked is available on the web site. During the Spring of 2004, I worked with Valery Alexeev and other students on a research project studying Higher Dimensional Analogues of Stable Curves using combinatorial and geometric techniques. During the 2004 academic year, I worked with Elham Izadi and other students on a research project studying Sheaves and Quivers. We investigated various properties of the derived categories of varieties and associated objects. During the Fall of 2006, I worked with Dino Lorenzini and other students on a research project studying the Critical Group of graphs. More information is available on the web site. Additionally I wrote some Maple code to do some calculations which can be found on my site. In the Spring of 2007, I worked with Valery Alexeev and other students on a research project studying the moduli space of branch varieties and related open problems.