Office Location: | 106 Physics Bldg |
Office Phone: | (919)-660-2816 |
Email Address: | |
Web Page: | http://math.duke.edu/~eekatz |
PhD | Stanford University | 2004 |
BS | The Ohio State University | 1999 |
Current projects: Piecewise Polynomials, Minkowski Weights, and Equivariant Cohomology
I study relative Gromov-Witten invariants and Tropical Geometry. I am particularly interested in enumerative problems (generalizations of statements of the form that there exists one line between two points or one conic between five points in the plane). Gromov-Witten theory has its origins in geometry but has very much a combinatorial feel. Tropical geometry is a simplified combinatorial model of algebraic geometry that nonetheless manages to capture much of its character. My research is in studying the moduli spaces that are used to compute Gromov-Witten invariants and finding ways to package the invariants. This work overlaps with Symplectic Geometry, the study of moduli of curves, and some areas of combinatorics. Currently, I am trying to systematize degeneration methods using ideas from tropical geometry. This will require developing the foundations of tropical intersection theory and applying them to a particular moduli space.