Research

Interests

Arithmetic Geometry

rational and integral points • Cox rings and torsors • local-to-global principles • Arakelov geometry • computer based and experimental methods

Preprints

 

  1. On everywhere locally soluble varieties in families over toric bases

    with Vladimir Mitankin, Leo Schäfer, and Damaris Schindler
    arXiv:2609.01825

  2. Equidistribution and the torsor method

    with Christian Bernert and Ulrich Derenthal
    arXiv:2607.14866

  3. Integral points over number fields: a Clemens complex jigsaw puzzle

    with Christian Bernert, Ulrich Derenthal, and Judith Ortmann
    to appear in Math. Z.
    arXiv:2601.08774

  4. Integral Diophantine approximation on varieties

    with Zhizhong Huang
    to appear in Algebr. Geom.
    arXiv:2509.03998
    interactive version of Figure 1: left (height at most 100), right (height at most 350)

 

Publications

 

  1. Iitaka fibrations and integral points: a family of arbitrarily polarized spherical threefolds

    with Ulrich Derenthal
    J. Lond. Math. Soc. 112 (6), 2025
    preprint: arXiv:2505.10245*

  2. Integral points on cubic surfaces: heuristics and numerics

    with Tim Browning
    Selecta Math. (N.S.) 31 (81), 1-65, 2025
    preprint: arXiv:2407.16315*
    code • data and notebooks

  3. Integral points of bounded height on a certain toric variety

    Trans. Amer. Math. Soc. Ser. B 11(2024), 567-599
    preprint: arXiv:2202.10909
    interactive version of Figure 1

  4. Integral points on singular del Pezzo surfaces

    with Ulrich Derenthal
    J. Inst. Math. Jussieu 23 (3), 1259–1294, 2024
    preprint: arXiv:2109.06778

  5. Integral points of bounded height on a log Fano threefold

    Int. Math. Res. Not. IMRN 8, 6780–6808, 2023
    preprint: arXiv:1901.08503

  6. Equidistribution and freeness on Grassmannians

    with Tim Browning and Tal Horesh
    Algebra Number Theory 16 (10), 2385–2407, 2022
    preprint: arXiv:2102.11552

*preprint differs from published version

 

PhD Thesis

 

Integral points of bounded height via universal torsors

doi:10.15488/9870, 2020