Research

My research interests are in arithmetic and algebraic geometry with a particular focus on tropical geometry and on moduli spaces. In order to relate tropical geometry to the classical world of algebraic geometry I am using techniques from non-Archimedean and logarithmic geometry.

My preprints are all on the arXiv. Feel free to check out my Google Scholar profile.

Preprints

  1. Realizability of tropical canonical divisors (joint with Martin Möller and Annette Werner)
  2. A moduli stack of tropical curves (joint with Renzo Cavalieri, Melody Chan, and Jonathan Wise)
  3. Non-Archimedean geometry of Artin fans

In press

  1. Logarithmic Picard groups, chip firing, and the combinatorial rank (joint with T. Foster, D. Ranganathan, and M. Talpo), Mathematische Zeitschrift, to appear.

Publications

  1. Clutching and gluing in tropical and logarithmic geometry (joint with Alana Huszar and Steffen Marcus). Journal of Pure and Applied Algebra, Volume 223, Issue 5, May 2019, Pages 2036-2061.
  2. Towards a tropical Hodge bundle (joint with Bo Lin). Combinatorial Algebraic Geometry, 353-368, Fields Institute Communications (2017), Volume 80, Springer 2017, Editors: Greg Smith and Bernd Sturmfels.
  3. Tropicalization is a non-Archimedean analytic stack quotient. Mathematical Research Letters 24 (2017) No. 4, 1205-1237.
  4. Functorial tropicalization of logarithmic schemes: The case of constant coefficients. Proceedings of the London Mathematical Society (2017) 114 (6), 1081-1113.
  5. Skeletons and fans of logarithmic structures (joint with D. Abramovich, Q. Chen, S. Marcus, and J. Wise). Non-Archimedean and Tropical Geometry, 287-336, Simons Symposia (2016), Editors: Matt Baker and Sam Payne.
  6. Faithful realizability of tropical curves (joint with M. Cheung, L. Fantini, and J. Park). Int. Math. Res. Notices (2016) 2016 (15): 4706-4727.
  7. Tropical geometry of moduli spaces of weighted stable curves. Journal of the London Mathematical Society (2015) 92 (2): 427-450.
  8. Tropical compactification in log-regular varieties. Mathematische Zeitschrift, June 2015, Volume 280, Issue 1-2, pp 195-210.

Collaborators

Dan Abramovich, Renzo Cavalieri, Melody Chan, Qile Chen, Man-Wai Cheung, Lorenzo Fantini, Tyler Foster, Alana Huszar, Bo Lin, Steffen Marcus, Martin Möller, Jennifer Park, Dhruv Ranganathan, Mattia Talpo, Annette Werner, Jonathan Wise

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