Eric 
Katz

Eric Katz

Assistant Professor
Combinatorics & Optimization Department
University of Waterloo

200 University Ave W
Waterloo, Ontario, Canada
N2L 3G1

Mathematics & Computer Building (MC) 6318
519-888-4567 x35295
eekatz (at) uwaterloo (dot) ca

Research
Press
Teaching
I am an Assistant Professor in the Department of Combinatorics and Optimization, cross-appointed to the Department of Pure Mathematics at the University of Waterloo. This fall, I will be taking an Assistant Professor position in the Department of Mathematics at The Ohio State University. I'm primarily interested in tropical geometry, arithmetic geometry, and combinatorial algebraic geometry. Before coming to Waterloo, I was as an RTG Postdoc at The University of Texas, a Postdoctoral member at Mathematical Sciences Research Institute, and an Assistant Research Professor at Duke University. I was a graduate student at Stanford University and an undergraduate at The Ohio State University.

My curriculum vitae is available here.

Research

Here are some slide presentations. In case you're wondering, "What is Tropical Geometry?"

My research statement (without future research plans).
  1. Hodge theory for combinatorial geometries (with Karim Adiprasito and June Huh), submitted.

  2. Uniform bounds for the number of rational points on curves of small Mordell-Weil rank (with Joseph Rabinoff and David Zureick-Brown), Duke Mathematical Journal, accepted.

  3. Tropical geometry, the motivic nearby fiber and limit mixed Hodge numbers of hypersurfaces (with Alan Stapledon), Research in the Mathematical Sciences, accepted.

  4. Local h-polynomials, invariants of subdivisions, and mixed Ehrhart theory (with Alan Stapledon), Adv. Math., 286 (2016), 181--239.

  5. Matroid theory for algebraic geometers, Simons Symposium Proceedings, accepted.

  6. A Non-Abelian Analogue of Whitney's 2-isomorphism theorem, J. Algebraic Combinatorics, 39 (2014), 683-690.

  7. The Chabauty-Coleman bound at a prime of bad reduction and clifford bounds for geometric rank functions (with David Zureick-Brown), Compositio Math. 149 (2013), 1818-1838.

  8. Tropical Realization Spaces for Polyhedral Complexes, Proceedings of the Workshop on Tropical Geometry. Contemp. Math. 589 (2013), 235-251.

  9. Log-concavity of characteristic polynomials and the Bergman fan of matroids (with June Huh), Math Ann. 354 (2012), 1103-1116.

  10. Obstructions to lifting tropical curves surfaces in 3-space (with Tristram Bogart), SIAM J. Discrete Math. 26 (2012), 1050-1067.

  11. Lifting Tropical Curves in Space and Linear Systems on Graphs, Adv. Math. 230 (2012), 853-875.

  12. Tropical Geometry and the Motivic Nearby Fiber (with Alan Stapledon), Compositio Math. 148 (2012), 269-294.

  13. Tropical Intersection Theory from Toric Varieties, Collect. Math. 63 (2012), 29-44.

  14. Realization Spaces for Tropical Fans (with Sam Payne), Proceedings of the Abel Symposium, vol. 6, 2011

  15. Monodromy Filtrations and the Topology of Tropical Varieties (with David Helm), Canadian J. Math. 64 (2011), 845-868.

  16. The tropical j-invariant (with Hannah Markwig and Thomas Markwig), LMS J. Comput. Math. 12 (2009), 275-294.

  17. A Tropical Toolkit, Expo. Math. 27 (2009) 1-36.

  18. Tropical Invariants from the Secondary Fan, (withdrawn).

  19. The j-invariant of a Plane Tropical Cubic (with Hannah Markwig and Thomas Markwig), J. Algebra 320 (2008) 3832-3848.

  20. Piecewise polynomials, Minkowski weights, and localization on toric varieties (with Sam Payne), Algebra Number Theory 2 (2008) 135-155.

  21. An Algebraic Formulation of Symplectic Field Theory, Journal of Symplectic Geometry 2 (2008) 135-155.

  22. Line-Bundles on Stacks of Relative Maps, unpublished note.

  23. Topological Recursion Relations by Localization, unpublished note.

Press

  1. Matt Baker's blog post on the effective Chabauty method describing my work with Zureick-Brown

  2. Departmental story about the proof of Rota's log-concavity conjecture by Adiprasito, Huh, and Katz

  3. Gil Kalai announces the proof of Rota's log-concavity conjecture by Adiprasito, Huh, and Katz

  4. Matt Baker's blog post on the proof of Rota's conjecture

  5. Article on the Chromatic Polynomial and Adiprasito-Huh-Katz from Nieuw Archief voor Wiskunde (in Dutch)

Teaching

Fall 2015:
  • CO 330: Combinatorial Enumeration
Office Hours: W 3:30-4:20

Warning: I cannot read the huge number of emails from students in my undergraduate classes. Non-emergency emails should be sent to the appropriate TA. I'm sorry, but in the interests of fairness, non-emergency emails addressed to me will not be answered or acknowledged. It's often best to talk to me before or after class or in my office hours. Emails to me will be logged for future reference.