


I am an Assistant Professor 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 the Ohio State University I was an Associate Professor in the Departments of Combinatorics and Optimization and Pure Mathematics at the University of Waterloo.
Prior to that, 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 of Matroids (with Karim Adiprasito and June Huh), Notices of the AMS, 64 (2017), 2630.
NewtonOkounkov Bodies over Discrete Valuation Rings (with Stefano Urbinati), submitted.
Diophantine and tropical geometry, and uniformity of rational points on curves (with Joseph Rabinoff and David ZureickBrown), submitted.
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, 165 (2016), 31893240.
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.
Teaching
I will be using carmen for all communication involving teaching.
Spring 2017:
 Math 2568: Linear Algebra
Office Hours: Wednesday 34pm, Thursday 23pm
Warning:
It's often hard to keep up with emails from students in my undergraduate
classes. If your email can be better answered in a brief chat with me, I'd
prefer that you talk to me before or after class or in my office hours.
Press

What is Tropical Geometry?, Notices of the AMS, 64 (2017), 380382.

Matt Baker's Current Events Bulletin talk on Hodge Theory in Combinatorics at 2017 JMM
Matt Baker's blog post on the effective Chabauty method describing my work with ZureickBrown
University of Waterloo story about the proof of Rota's conjecture by Adiprasito, Huh, and Katz
Gil Kalai announces the proof of Rota's 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)
Please note that Adiprasito, Huh, and Katz resolved Rota's logconcavity conjecture which is distinct from Rota's excluded minors for matroids conjecture, a problem considered to be important by the structural combinatorics community.
