Manuscripts (arXiv, GoogleScholar)

• Logarithmic Donaldson-Thomas theory. With D. Maulik.

• Gromov-Witten theory with maximal contacts. With N. Nabijou.

• A note on cycles of curves in a product of pairs.

• Curve counting in genus one: elliptic singularities & relative geometry. With L. Battistella & N. Nabijou.

• Logarithmic Gromov-Witten theory with expansions. See also the Oberwolfach Report and Notes for a talk at ETH.

• Brill-Noether theory for curves of a fixed gonality. With D. Jensen. See also Sam Payne's notes.

Publications

• Curve counting on toric surfaces: tropical geometry & the Fock space. With R. Cavalieri, P. Johnson, & H. Markwig. In Mathematical Proceedings of the Cambridge Philosophical Society.

• Rational curves in the logarithmic multiplicative group. With J. Wise. In Proceedings of the American Mathematical Society.

• Moduli of stable maps in genus one & logarithmic geometry II. With K. Santos-Parker & J. Wise. In Algebra & Number Theory.

• Moduli of stable maps in genus one & logarithmic geometry I. With K. Santos-Parker & J. Wise. In Geometry & Topology. See also Jonathan's Notes.

• Topology of tropical moduli of weighted stable curves. With A. Cerbu, S. Marcus, L. Peilen, & A. Salmon. In Advances in Geometry.

• Motivic Hilbert zeta functions of curves are rational. With D. Bejleri & R. Vakil. In Journal of the Institute of Mathematics, Jussieu.

• Incidence geometry and universality in the tropical plane. With M. Brandt, M. Jones, & C. Lee. In Journal of Combinatorial Theory, Series A.

• Logarithmic Picard groups, chip firing, and the combinatorial rank. With T. Foster, M. Talpo, & M. Ulirsch. In Mathematische Zeitschrift.

• Skeletons of stable maps II: superabundant geometries. In Research in the Mathematical Sciences.

• A note on Brill-Noether existence for graphs of low genus. With S. Atanasov. In Michigan Mathematical Journal.

• A graphical interface for the Gromov-Witten theory of curves. With R. Cavalieri, P. Johnson, & H. Markwig. In Algebraic Geometry: Salt Lake City 2015.

• Tropical Hurwitz numbers. With H. Markwig. Appendix to A First Course in Hurwitz theory by Cavalieri and Miles.

• Enumerative geometry of elliptic curves on toric surfaces. With Y. Len. In Israel Journal of Mathematics.

• Degenerations of toric varieties over valuation rings. With T. Foster. In Bulletin of the London Mathematical Society

• Skeletons of stable maps I: rational curves in toric varieties. In Journal of the London Mathematical Society

• Superabundant curves and the Artin fan. In International Mathematics Research Notices.

• Hahn analytification and connectivity of higher rank tropical varieties. With T. Foster. In Manuscripta Mathematica.

• Toric graph associahedra and compactifications of M0,n. With R. Ferreira da Rosa & D. Jensen. In Journal of Algebraic Combinatorics

• Realization of groups with pairing as Jacobians of finite graphs. With L. Gaudet, D. Jensen, N. Wawrykow, & T. Weisman. In Annals of Combinatorics.

• Tropical compactification and the Gromov-Witten theory of P1. With R. Cavalieri & H. Markwig. In Selecta Mathematica.

• Moduli spaces of rational weighted stable curves and tropical geometry. With R. Cavalieri, S. Hampe, & H. Markwig. In Forum of Mathematics (Sigma)

• Tropicalizing the space of admissible covers. With R. Cavalieri & H. Markwig. In Mathematische Annalen.

• Brill-Noether theory of maximally symmetric graphs. With T. Leake. In European Journal of Combinatorics.

• Gromov-Witten theory of P1xP1xP1. With D. Karp. In Journal of Pure and Applied Algebra.

• Toric Symmetry of CP3. With D. Karp, P. Riggins, & U. Whitcher. In Advances in Theoretical and Mathematical Physics.

Theses

• Skeletons, degenerations, & Gromov-Witten theory. 2016 Doctoral thesis, Yale University.

• Gromov-Witten theory of blowups of toric threefolds 2012 Undergraduate thesis, Harvey Mudd College.

Unpublished Notes

• Analytification and tropicalization over Z. I establish Sam's inverse limit over the integers. I never found an application, but take a look at this for inspiration.

• Toric Severi degrees are logarithmic Gromov-Witten invariants. Sam asked me if the logarithmic GW invariants of toric surfaces were enumerative.

• The well-spacedness equation. Proves Speyer's realizability theorem tropical curves via deformation theory. It is self-contained but substantially subsumed by this.