**Papers under review (arXiv, GoogleScholar)**

- Motivic Hilbert zeta functions of curves are rational. With D. Bejleri & R. Vakil
*.* **Moduli of stable maps in genus one & logarithmic geometry II**. With K. Santos-Parker & J. Wise*.*- Moduli of stable maps in genus one & logarithmic geometry I. With K. Santos-Parker & J. Wise.
**Incidence geometry and universality in the tropical plane.**With M. Brandt, M. Jones, & C. Lee**.**- Topology of tropical moduli of weighted stable curves. With A. Cerbu, S. Marcus, L. Peilen, & A. Salmon.
- 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 these notes.

**Publications**

- 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 M
_{0,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 P
^{1}. 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 P
^{1}xP^{1}xP^{1}. With D. Karp. In*Journal of Pure and Applied Algebra**.* - Toric Symmetry of CP
^{3}. 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.

**In Preparation**

My ongoing projects include the following. In a project with Markwig, I am working towards a determination of the logarithmic Gromov-Witten theory of toric varieties in genus 0, including descendant insertions. Our methods combine enhancements of well-known tropical computational tools known as floor diagrams, with structural results about the space of logarithmic stable maps in genus 0, proved in my thesis. Our long term target is an all genus recursive determination of the descendant theory of toric varieties using a generalization of double ramification cycle. I am also completing work on a tropical degeneration formula for the genus 1 enumerative invariants of toric varieties, building on earlier work with Santos-Parker and Wise. I am also trying to find alternate approaches in simpler situations to the logarithmic decomposition formula of Abramovich-Chen-Gross-Siebert. A longer term project, still in its infancy, is an alternative method towards the full degeneration and localization formulas in logarithmic Gromov-Witten theory, by "sheaffification in the topology of toroidal modifications". If you'd like to know more about any of these ideas, email me!