Publications, Preprints & Theses

Publications

  • “Poincaré duality for the tropical Dolbeault cohomology of non-archimedean Mumford curves” with V. Wanner
    Journal of Number Theory
    Publication available online here. DOI: 10.1016/j.jnt.2017.11.004
    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. DOI: 10.1007/s00209-015-1583-8
    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
  • “Poincaré duality for the tropical Dolbeault cohomology of non-archimedean curves”
    arxiv:1706.05895 Last update: 12/2017
  • “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” (Weil Conjectures for Curves over Finite Fields)