## Research & Publications

**Manuscripts (arXiv, GoogleScholar)**

**Gromov-Witten theory of hypersurfaces in genus one.**With L. Battistella and N. Nabijou. In preparation.**Gromov-Witten theory with expansions**. Draft.**Rational curves in the logarithmic multiplicative group****.**With J. Wise**Moduli of stable maps in genus one & logarithmic geometry I**. With K. Santos-Parker & J. Wise.**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**.

**Publications **

**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 M**. With R. Ferreira da Rosa & D. Jensen. In_{0,n}**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**. With R. Cavalieri & H. Markwig. In^{1}**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**. With D. Karp. In^{1}xP^{1}xP^{1}**Journal of Pure and Applied Algebra**.**Toric Symmetry of CP**. With D. Karp, P. Riggins, & U. Whitcher. In^{3}.**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**.