Research Interests
My research interests are in the tropical geometry of moduli spaces and its applications to classical questions in arithmetic and algebraic geometry. Given an algebraic geometric moduli problem, the basic idea is to first study the geometry of its tropical analogue, a polyhedral shadow of the original situation, and then to use techniques from nonArchimedean geometry and from logarithmic geometry to lift the insights gained this way back from the combinatorics to the world of algebraic geometry. Here is a list of buzzwords that will surely spark my interest:
 Tropical and nonArchimedean geometry
 Logarithmic and toric geometry
 Moduli spaces and stacks
 Picard varieties and BrillNoether theory
Preprints
 Realizability of tropical canonical divisors (joint with Martin Möller and Annette Werner)
 Clutching and gluing in tropical and logarithmic geometry (joint with Alana Huszar and Steffen Marcus)
 A moduli stack of tropical curves (joint with Renzo Cavalieri, Melody Chan, and Jonathan Wise)
 NonArchimedean geometry of Artin fans
In press
 Logarithmic Picard groups, chip firing, and the combinatorial rank (joint with T. Foster, D. Ranganathan, and M. Talpo), Mathematische Zeitschrift, to appear.
 Towards a tropical Hodge bundle (joint with Bo Lin), Fields 2016 CAG book, to appear.
 Tropicalization is a nonArchimedean analytic stack quotient, Mathematical Research Letters, to appear.
Publications
 Functorial tropicalization of logarithmic schemes: The case of constant coefficients, Proceedings of the London Mathematical Society (2017) 114 (6), 10811113.
 Skeletons and fans of logarithmic structures (joint with D. Abramovich,
Q. Chen, S. Marcus, and J. Wise), NonArchimedean and Tropical Geometry, Simons Symposia (2016), Editors: Matt Baker and Sam Payne, pp. 287336.
 Faithful realizability of tropical curves (joint with M. Cheung, L. Fantini, and J. Park), Int. Math. Res. Notices (2016) 2016 (15): 47064727.
 Tropical geometry of moduli spaces of weighted stable curves, Journal of the London Mathematical Society (2015) 92 (2): 427450.
 Tropical compactification in logregular varieties, Mathematische
Zeitschrift, June 2015, Volume 280, Issue 12, pp 195210.
Nonrefereed publications, theses, and reports
 NewtonOkounkov bodies and reified valuations of higher rank (joint with A. Camara, I. Giné, R. Gualdi, N. Kalinin, J. Roé, S. Urbinati, and X. Xarles), Research Perspectives CRM Barcelona, to appear.

Logarithmic structures, Artin fans, and tropical compactifications, Oberwolfach Reports Volume 12, Issue 4, 2015, pp. 3271–3331.
 Tropical geometry of logarithmic schemes, my PhDThesis