


As of August 1, 2016, I am an Assistant Professor position in the
Department of Mathematics at The Ohio
State University. My new website will be here.
Prior to that I was an Associate Professor in the Department of Combinatorics and Optimization, crossappointed to the Department of Pure Mathematics at the University of Waterloo.
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. Needless to say, Go Bucks!
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).
Hodge theory for combinatorial
geometries (with Karim Adiprasito and June Huh), submitted.
Uniform bounds for the number of rational points on
curves of small MordellWeil rank (with Joseph Rabinoff and David
ZureickBrown), Duke Mathematical Journal, accepted.
Tropical geometry, the motivic nearby fiber and limit
mixed Hodge numbers of hypersurfaces (with Alan Stapledon), Research in the Mathematical Sciences, 3:10 (2016).
Local hpolynomials, invariants of subdivisions, and
mixed Ehrhart theory (with Alan Stapledon), Adv. Math.,
286 (2016), 181239.
Matroid theory for algebraic geometers, Simons Symposium Proceedings, accepted.
A NonAbelian Analogue of Whitney's 2isomorphism theorem, J. Algebraic Combinatorics, 39 (2014), 683690.
The ChabautyColeman bound at a prime of bad reduction and clifford bounds for geometric rank functions (with David ZureickBrown), Compositio Math. 149 (2013), 18181838.
Tropical Realization Spaces for Polyhedral Complexes, Proceedings of the Workshop on Tropical Geometry. Contemp. Math. 589 (2013), 235251.
Logconcavity of characteristic
polynomials and the Bergman fan of matroids (with June Huh), Math Ann. 354 (2012), 11031116.
Obstructions to lifting tropical curves surfaces in 3space (with Tristram Bogart), SIAM J. Discrete Math. 26 (2012), 10501067.
Lifting Tropical Curves in Space and Linear Systems on Graphs, Adv. Math. 230 (2012), 853875.
Tropical Geometry and the Motivic Nearby Fiber (with Alan Stapledon), Compositio Math. 148 (2012), 269294.
Tropical Intersection Theory from Toric Varieties, Collect. Math. 63 (2012), 2944.
Realization Spaces for Tropical Fans (with Sam Payne), Proceedings of the Abel Symposium, vol. 6, 2011
Monodromy Filtrations and the Topology of Tropical Varieties (with David Helm), Canadian J. Math. 64 (2011), 845868.
The tropical jinvariant (with Hannah Markwig and Thomas Markwig), LMS J. Comput. Math. 12 (2009), 275294.
A Tropical Toolkit, Expo. Math. 27 (2009) 136.
Tropical Invariants from the Secondary Fan, (withdrawn).
The jinvariant of a Plane Tropical Cubic (with Hannah Markwig and Thomas Markwig), J. Algebra 320 (2008) 38323848.
Piecewise polynomials, Minkowski weights, and localization on toric varieties (with Sam Payne), Algebra Number Theory 2 (2008) 135155.
An Algebraic Formulation of Symplectic Field Theory, Journal of Symplectic Geometry 2 (2008) 135155.
LineBundles on Stacks of Relative Maps, unpublished note.
Topological Recursion Relations by Localization, unpublished note.
Press
Matt Baker's blog post on the effective Chabauty method describing my work with ZureickBrown
Departmental story about the proof of Rota's logconcavity conjecture by Adiprasito, Huh, and Katz
Gil Kalai announces the proof of Rota's logconcavity conjecture by Adiprasito, Huh, and Katz
Matt Baker's blog post on the proof of Rota's conjecture
Article on the Chromatic Polynomial and AdiprasitoHuhKatz from Nieuw Archief voor Wiskunde (in Dutch)
Teaching
Fall 2015:
 CO 330: Combinatorial Enumeration
Office Hours:
W 3:304:20
Warning:
I cannot read the huge number of emails from students in my
undergraduate classes. Nonemergency emails should be sent to
the appropriate TA. I'm sorry, but in the interests of fairness,
nonemergency 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.
