Eric E. Katz, Named 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 math.utexas.edu Missing you all.
 Education:
PhD  Stanford University  2004 
BS  The Ohio State University  1999 
 Research Interests: Algebraic and Symplectic Geometry
Current projects:
Piecewise Polynomials, Minkowski Weights, and Equivariant Cohomology
I study relative GromovWitten 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). GromovWitten 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 GromovWitten 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 GromovWitten Invariants, Tropical Geometry
 Keywords:
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, LineBundles on Stacks of Relative Maps
(Preprint, 2005) [math.AG/0507322] [abs] [author's comments]
 Eric Edward Katz, Formalism for Relative GromovWitten 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]
