In Preparation
The Universal Deformation Variety of a 3-manifold (with Henry Segerman)
Counting Tropical Curves on Abelian Surfaces (with David Helm)
Tropical Linear System on Surfaces (with Christian Haase, Gregg Musiker, and Alan Stapledon)
A Cohomological Approach to Linear Systems on Graphs
Submitted Articles
Obstructions to Lifting Tropical Curves in Hypersurfaces (with Tristram Bogart)
preprint, 2011
Tropical Realization Spaces and Tropical Approximation
preprint, 2010
Lifting Tropical Curves in Space and Linear Systems on Graphs
preprint, 2010
Publications
Tropical Geometry and the Motivic Nearby Fiber (with Alan Stapledon)
Compositio Math., to appear
Realization Spaces for Tropical Fans (with Sam Payne)
Proceedings of the Abel Symposium, to appear
Monodromy Filtrations and the Topology of Tropical Varieties (with David Helm)
Canadian J. Math., to appear
Tropical Intersection Theory from Toric Varieties
Collect. Math., to appear
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
Adv. Geom. 9 (2009) 153-180.
The j-invariant of a Plane Tropical Cubic (with Hannah Markwig and Thomas Markwig)
J. Alg. 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.
Unpublished Manuscripts (from grad school work)
Line-Bundles on Stacks of Relative Maps
Topological Recursion Relations by Localization