Hodge theory for combinatorial
geometries (with Karim Adiprasito and June Huh), submitted.
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.
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 h-polynomials, invariants of subdivisions, and
mixed Ehrhart theory (with Alan Stapledon), Adv. Math.,
286 (2016), 181--239.
Matroid theory for algebraic geometers, Simons Symposium Proceedings, accepted.
A Non-Abelian Analogue of Whitney's 2-isomorphism theorem, J. Algebraic Combinatorics, 39 (2014), 683-690.
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.
Tropical Realization Spaces for Polyhedral Complexes, Proceedings of the Workshop on Tropical Geometry. Contemp. Math. 589 (2013), 235-251.
Log-concavity of characteristic
polynomials and the Bergman fan of matroids (with June Huh), Math Ann. 354 (2012), 1103-1116.
Obstructions to lifting tropical curves surfaces in 3-space (with Tristram Bogart), SIAM J. Discrete Math. 26 (2012), 1050-1067.
Lifting Tropical Curves in Space and Linear Systems on Graphs, Adv. Math. 230 (2012), 853-875.
Tropical Geometry and the Motivic Nearby Fiber (with Alan Stapledon), Compositio Math. 148 (2012), 269-294.
Tropical Intersection Theory from Toric Varieties, Collect. Math. 63 (2012), 29-44.
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), 845-868.
The tropical j-invariant (with Hannah Markwig and Thomas Markwig), LMS J. Comput. Math. 12 (2009), 275-294.
A Tropical Toolkit, Expo. Math. 27 (2009) 1-36.
Tropical Invariants from the Secondary Fan, (withdrawn).
The j-invariant of a Plane Tropical Cubic (with Hannah Markwig and Thomas Markwig), J. Algebra 320 (2008) 3832-3848.
Piecewise polynomials, Minkowski weights, and localization on toric varieties (with Sam Payne), Algebra Number Theory 2 (2008) 135-155.
An Algebraic Formulation of Symplectic Field Theory, Journal of Symplectic Geometry 2 (2008) 135-155.
Line-Bundles on Stacks of Relative Maps, unpublished note.
Topological Recursion Relations by Localization, unpublished note.