## Research & Publications

I am broadly interested in algebraic geometry, with a focus on the use of logarithmic and tropical methods to establish results about the geometry of curves, moduli spaces, and enumerative geometry. A complete list of papers and preprints can be found **here** and my papers are available on **arXiv****, GoogleScholar**.

**Selected Publications and Preprints**

**Logarithmic Gromov-Witten theory with expansions (2019).***(Under review)***Moduli of stable maps in genus one & logarithmic geometry, Volumes I & II (2017)****.**These two papers, written jointly with Keli Santos-Parker and Jonathan Wise, provide a reworking of the foundations of the theory of stable maps in genus one. We use tropical methods to realize a connection between earlier work of Smyth and Vakil-Zinger, leading to the systematic introduction of elliptic singularities into the stable maps theory. We apply this to construct moduli theoretic desingularizations of various spaces of genus one curves.*(Volume I in Geometry & Topology, Volume II under review)***Brill-Noether theory for curves of a fixed gonality (2017)****.**The Brill-Noether theorem governs the complexity of embeddings of smooth algebraic curves in projective space, when the complex structure on the curve is general. This paper, written with Dave Jensen, is a generalization of this theorem for curves which are general within a prescribed special locus. More precisely, for curves that are general of a fixed gonality. The result was conjectured in earlier work of Pflueger, and is a broad generalization of a classical theorem of Clifford on hyperelliptic curves.*(Under review)***Skeletons of stable maps I: rational curves in toric varieties (2016)****.**This paper constructs the moduli space of logarithmic stable maps from genus 0 curves to toric varieties*(Journal of the London Mathematical Society)***Tropicalizing the space of admissible covers (2014)****.**The moduli space of admissible covers is a compactification of the Hurwitz scheme. In this paper with Renzo Cavalieri and Hannah Markwig, we identify a precise relationship between the non-archimedean analytic skeleton of this space and a tropical moduli space, using a framework outlined by Abramovich-Caporaso-Payne.*(Mathematische Annalen)*