Publications, Preprints & Theses

Publications

  • Tropical Hodge numbers of non-archimedean curves
    To appear in Israel Journal of Mathematics
    arxiv:1706.05895
  • Poincaré duality for the tropical Dolbeault cohomology of non-archimedean Mumford curves
    with V. Wanner
    Journal of Number Theory 187, 344-371, Publication available online here.
    arxiv:1612.01889
  • Superforms, Tropical Cohomology, and Poincaré Duality
    with K. Shaw and J. Smacka
    To appear in Advances in Geometry
    arXiv:1512.07409 Last update: 03/2017
  • 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

  • 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
    arxiv:1712.00980 Last update: 12/2017
  • Lefschetz (1,1)-theorem in tropical geometry
    with J. Rau and K. Shaw
    arxiv:1711.07900
  • 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
    arXiv:1608.01919 Last update: 10/2017

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)