Research & Publications
- Gromov-Witten theory with expansions. Draft version from June 2018.
- Moduli of stable maps in genus one & logarithmic geometry I. With K. Santos-Parker & J. Wise. In revision.
- Moduli of stable maps in genus one & logarithmic geometry II. With K. Santos-Parker & J. Wise.
- Curve counting on toric surfaces: tropical geometry & the Fock space. With R. Cavalieri, P. Johnson, & H. Markwig.
- Brill-Noether theory for curves of a fixed gonality. With D. Jensen. See also Sam Payne's notes.
- Topology of tropical moduli of weighted stable curves. With A. Cerbu, S. Marcus, L. Peilen, & A. Salmon. Advances in Geometry.
- Motivic Hilbert zeta functions of curves are rational. With D. Bejleri & R. Vakil. Journal of the Institute of Mathematics, Jussieu.
- Incidence geometry and universality in the tropical plane. With M. Brandt, M. Jones, & C. Lee. 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.
- Skeletons, degenerations, & Gromov-Witten theory. 2016 Doctoral thesis, Yale University.
- Gromov-Witten theory of blowups of toric threefolds 2012 Undergraduate thesis, Harvey Mudd College.
- 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.