Research interests

Algebraic Geometry and its relations to Complex Geometry, Complex Analysis and Commutative Algebra. More specifically:

  • Uniformization of Kähler spaces
  • Singularities in positive characteristic
  • Algebraic approximation of Kähler manifolds
  • Lipman–Zariski conjecture
  • Differential forms on singular spaces

Publications

Preprints / submitted

  1. (with Aryaman Patel) Slope zero tensors, uniformizing variations of Hodge structure and quotients of tube domains [arXiv]
  2. (with Aryaman Patel) Semispecial tensors and quotients of the polydisc [arXiv]
  3. (with Aryaman Patel) Uniformization of klt pairs by bounded symmetric domains [arXiv]
  4. (with Junyan Cao, Philipp Naumann, Mihai Păun, Thomas Peternell and Xiaojun Wu) Hermite–Einstein metrics in singular settings [arXiv]

Published

  1. (with Benoît Claudon and Henri Guenancia) Equality in the Miyaoka–Yau inequality and uniformization of non-positively curved klt pairs, C. R. Math. Acad. Sci. Paris 362 (2024), Special issue in memory of Jean-Pierre Demailly, pp. 55–81 [arXiv] [doi]
  2. The Violation of the Lipman–Zariski conjecture in positive characteristic, J. Algebra 601 (2022), pp. 115–128 [arXiv] [doi]
  3. (with Benoît Claudon and Henri Guenancia) Numerical characterization of complex torus quotients, Comment. Math. Helv. 97 (2022), pp. 769–799 [arXiv] [doi]
  4. A decomposition theorem for singular Kähler spaces with trivial first Chern class of dimension at most four, Ann. Fac. Sci. Toulouse Math. 32 (2023), pp. 893–909 [arXiv] [doi]
  5. (with Benoît Claudon, Henri Guenancia and Philipp Naumann) Kähler spaces with zero first Chern class: Bochner principle, Albanese map and fundamental groups, J. Reine Angew. Math. (Crelle) 786 (2022), pp. 245–275 [arXiv] [doi]
  6. (with Martin Schwald) The Kodaira problem for Kähler spaces with vanishing first Chern class, Forum of Mathematics, Sigma 9 (2021), e24 [arXiv] [doi]
  7. Differential forms on log canonical spaces in positive characteristic, J. London Math. Soc. 104 (2021), pp. 2208–2239 [arXiv] [doi]
  8. A note on Flenner's extension theorem, manuscripta math. 165 (2021), pp. 597–603 [arXiv] [doi]
  9. (with Hannah Bergner) The Lipman–Zariski conjecture in genus one higher, Forum of Mathematics, Sigma 8 (2020), e21 [arXiv] [doi]
  10. (with Martin Schwald) On the Kodaira problem for uniruled Kähler spaces, Arkiv för Matematik 58 (2020), pp. 267–284 [arXiv] [doi]
  11. The Lipman–Zariski conjecture in low genus, IMRN 2021, pp. 426–441 [arXiv] [doi]
  12. (with Tim Kirschner) Finite quotients of three-dimensional complex tori, Ann. Inst. Fourier (Grenoble) 70 (2020), pp. 881–914 [arXiv] [doi]
  13. (with Bhargav Bhatt, Javier Carvajal-Rojas, Karl Schwede and Kevin Tucker) Étale fundamental groups of strongly F-regular schemes, IMRN 2019, pp. 4325–4339 [arXiv] [doi]
  14. (with Karl Schwede) Discreteness of F-jumping numbers at isolated non-$\mathbb Q$-Gorenstein points, Proc. Amer. Math. Soc. 146 (2018), pp. 473–487 [arXiv] [doi]
  15. Algebraic approximation of Kähler threefolds of Kodaira dimension zero, Math. Annalen 371 (2018), pp. 487–516 [arXiv] [doi]
  16. A Mehta–Ramanathan theorem for linear systems with basepoints, Math. Nachrichten 289 (2016), pp. 1208–1218 [arXiv] [doi]
  17. The jumping coefficients of non-$\mathbb Q$-Gorenstein multiplier ideals, J. Algebra 450 (2016), pp. 323–348 [arXiv] [doi]
  18. The generalized Lipman–Zariski problem, Math. Annalen 362 (2015), pp. 241–264 [arXiv] [doi]
  19. (with Sándor J. Kovács) Potentially Du Bois spaces, J. Singularities 8 (2014), pp. 117–134 [arXiv] [doi]
  20. (with Sándor J. Kovács) An optimal extension theorem for 1-forms and the Lipman–Zariski conjecture, Documenta Math. 19 (2014), pp. 815–830 [arXiv] [doi]
  21. Bogomolov–Sommese vanishing on log canonical pairs, J. Reine Angew. Math. (Crelle) 702 (2015), pp. 109–142 [arXiv] [doi]

Theses

  • Kähler spaces with vanishing Chern classes, extension theorems for differential forms and the Lipman–Zariski conjecture, Habilitation thesis, University of Bayreuth, 2022 [available on request]
  • Differential forms on singular spaces, PhD thesis, University of Freiburg, 2013 [FreiDok]
  • Deformationen von Morphismen in Räume mit Quotientensingularitäten (Deformations of morphisms to spaces with quotient singularities), Diploma thesis, University of Cologne, 2009 [available on request]

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