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Eric E. Katz, Assistant Research Professor

Eric E. Katz

Please note: Eric has left the Mathematics department at Duke University; some info here might not be up to date.

Contact Info:
Office Location:  106 Physics Bldg
Office Phone:  (919)-660-2816
Email Address: send me a message
Web Page:  http://math.duke.edu/~eekatz

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:

PhDStanford University2004
BSThe Ohio State University1999
Research Interests: Algebraic and Symplectic Geometry

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.

Areas of Interest:

Relative Gromov-Witten Invariants, Tropical Geometry

Keywords:

Algebraic Geometry, Symplectic Geometry

Recent Publications

  1. Eric Katz, The Tropical Degree of Cones in the Secondary Fan (Preprint, 2006) [math.AG/0604290]
  2. Eric Katz, A Tropical Toolkit (Preprint, 2006) [math.AG/0610878]  [abs]
  3. Eric Edward Katz, Line-Bundles on Stacks of Relative Maps (Preprint, 2005) [math.AG/0507322]  [abs] [author's comments]
  4. Eric Edward Katz, Formalism for Relative Gromov-Witten Invariants, Journal of Symplectic Geometry (Accepted, 2005) [math.AG/0507321]  [abs] [author's comments]
  5. Eric Edward Katz, Topological Recursion Relations by Localization (Preprint, 2003) [math.AG/0310050]  [author's comments]

 

dept@math.duke.edu
ph: 919.660.2800
fax: 919.660.2821

Mathematics Department
Duke University, Box 90320
Durham, NC 27708-0320