Research

My research is mainly concerned with the algebraic geometry of curves and their moduli spaces.  When I was a graduate student, this meant that I studied Gromov-Witten theory, in which one attempts to answer enumerative questions (like "how many conics pass through a given set of five points in the plane?") using techniques motivated by theoretical physics.  More recently, it means that I study the moduli space of curves and its variants as interesting varieties in their own right, including their connections to combinatorics.

I have written a number of expository documents, at various levels of mathematical specialization, for those interested in learning more about this research area.  The article Gromov-Witten Theory: From curve counts to string theory (which appeared in the book Surveys on Recent Developments in Algebraic Geometry) is aimed at those with some background in algebraic geometry, while the article From counting curves to quantum physics is intended for undergraduate math students.