Publications, Preprints & Theses

Publications

  • Differentiability of non-archimedean volumes and non-archimedean Monge-Ampère equations (with an appendix by Rober Lazarsfeld)
    with J. I. Burgos Gil, W. Gubler, K. Künnemann and F. Martin
    to appear in Algebraic Geometry
    arXiv:1608.01919 Last update: 03/2019
  • Continuity of plurisubharmonic envelopes in non-archimedean geometry and test ideals (with an appendix by José Ingnacio Burgos Gil and Martín Sombra)
    with W. Gubler, K. Künnemann and F. Martin
    to appear in Annales de l’Institut Fourier
    arxiv:1712.00980 Last update: 11/2018
  • Tropical Dolbeault cohomology of non-archimedean curves and harmonic tropicalizations,
    available here.
    to appear in Oberwolfach Reports.
  • Tropical Hodge numbers of non-archimedean curves
    Israel Journal of Mathematics 229 (2019), 1-19, no.1, 287-305, Publication available online here.
    arxiv:1706.05895
  • Superforms, Tropical Cohomology, and Poincaré Duality
    with K. Shaw and J. Smacka
    Advances in Geometry 19 (2019), no. 1, 101-130, Publication available online here.
    arXiv:1512.07409
  • Lefschetz (1,1)-theorem in tropical geometry
    with J. Rau and K. Shaw
    Epijournal de Géometrie Algébrique, volume 2, article no. 11 (2018)
    arxiv:1711.07900
  • Poincaré duality for the tropical Dolbeault cohomology of non-archimedean Mumford curves
    with V. Wanner
    Journal of Number Theory 187 (2018), 344-371, Publication available online here.
    arxiv:1612.01889
  • A Poincaré lemma for real-valued differential forms on Berkovich spaces
    Mathematische Zeitschrift 282(3-4): 1149-1167, 2016, Publication available online here.
    arXiv:1409.0676

Preprints 

  • Real tropicalization and analytification of semialgebraic sets,
    with C. Scheiderer and J. Yu
    arxiv:1810.05132
  • Constructing smooth and fully faithful tropicalizations for Mumford curves,
    arxiv:1805.11594 Last update 04/2019

Theses

  • PhD Thesis: Real-valued differential forms on Berkovich analytic spaces and their cohomology,
    Published online, available here.
  • Cambridge Part III Essay: Arakelov Theory and Arithmetic Surfaces
  • Bachelor’s Thesis: Die Weil-Vermutungen für Kurven über endlichen Körpern (The Weil Conjectures for Curves over Finite Fields)