Eric E. Katz, Assistant Research Professor
Please note: Eric has left the Mathematics department at Duke University; some info here might not be up to date.
- Contact Info:
- Office Hours:
- I've moved to University of Texas in Austin.
My email is the username you'd expect at
Missing you all.
|BS||The Ohio State University||1999|
- Research Interests: Algebraic and Symplectic Geometry
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.
- Areas of Interest:
- Relative Gromov-Witten Invariants, Tropical Geometry
- Algebraic Geometry, Symplectic Geometry
- Recent Publications
- Eric Katz, The Tropical Degree of Cones in the Secondary Fan
(Preprint, 2006) [math.AG/0604290]
- Eric Katz, A Tropical Toolkit
(Preprint, 2006) [math.AG/0610878] [abs]
- Eric Edward Katz, Line-Bundles on Stacks of Relative Maps
(Preprint, 2005) [math.AG/0507322] [abs] [author's comments]
- Eric Edward Katz, Formalism for Relative Gromov-Witten Invariants,
Journal of Symplectic Geometry
(Accepted, 2005) [math.AG/0507321] [abs] [author's comments]
- Eric Edward Katz, Topological Recursion Relations by Localization
(Preprint, 2003) [math.AG/0310050] [author's comments]