Research Interests

My research interests are in arithmetic and algebraic geometry, in particular:

  • Tropical and Non-Archimedean Geometry
  • Logarithmic and Toric Geometry
  • Moduli Spaces and Deformation Theory
  • Algebraic, Analytic, and Combinatorial Stacks

Preprints

  1. A moduli stack of tropical curves (joint with Renzo Cavalieri, Melody Chan, and Jonathan Wise)
  2. Logarithmic Picard groups, chip firing, and the combinatorial rank (joint with T. Foster, D. Ranganathan, and M. Talpo)
  3. Non-Archimedean geometry of Artin fans

In press

  1. Towards a tropical Hodge bundle (joint with Bo Lin), Fields 2016 CAG book, to appear.
  2. Tropicalization is a non-Archimedean analytic stack quotient, Mathematical Research Letters, to appear.

Publications

  1. Functorial tropicalization of logarithmic schemes: The case of constant coefficients, Proceedings of the London Mathematical Society (2017) 114 (6), 1081-1113.
  2. Skeletons and fans of logarithmic structures (joint with D. Abramovich, Q. Chen, S. Marcus, and J. Wise), Non-Archimedean and Tropical Geometry, Simons Symposia (2016), Editors: Matt Baker and Sam Payne, pp. 287-336.
  3. Faithful realizability of tropical curves (joint with M. Cheung, L. Fantini, and J. Park), Int. Math. Res. Notices (2016) 2016 (15): 4706-4727.
  4. Tropical geometry of moduli spaces of weighted stable curves, Journal of the London Mathematical Society (2015) 92 (2): 427-450.
  5. Tropical compactification in log-regular varieties, Mathematische Zeitschrift, June 2015, Volume 280, Issue 1-2, pp 195-210.

Non-refereed publications, theses, and reports

  1. Newton-Okounkov 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.
  2. Logarithmic structures, Artin fans, and tropical compactifications, Oberwolfach Reports Volume 12, Issue 4, 2015, pp. 3271–3331.
  3. Tropical geometry of logarithmic schemes, my PhD-Thesis