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Papers

1. The monodromy of families of subvarieties on abelian varieties (joint with Thomas Krämer, Christian Lehn, and Marco Maculan). (arxiv)
   Submitted.
2. Smooth hypersurfaces in abelian varieties over arithmetic rings (joint with Siddharth Mathur) (arxiv, journal)
   Forum of Mathematics, Sigma, 10, E97.
3. Hilbert irreducibility for varieties with a nef tangent bundle (arxiv).
   Submitted.
4. Finiteness of non-constant maps over number fields (arxiv, journal).
   Math. Res. Lett., to appear.
5. Algebraic intermediate hyperbolicities (joint with Antoine Etesse and Erwan Rousseau) (arxiv)
   Submitted.
6. Hilbert's irreducibility theorem for abelian varieties (joint with Pietro Corvaja, Julian Lawrence Demeio, Davide Lombardo, and Umberto Zannier) (arxiv)
   Compositio Math., to appear.
7. Albanese maps and fundamental groups of varieties with many rational points over function fields (joint with Erwan Rousseau) (arxiv, journal)
   IMRN, to appear.
8. Good reduction and cyclic covers (joint with Daniel Loughran and Siddharth Mathur) (arxiv)
   J. Inst. Math. Jussieu, to appear.
9. The Shafarevich conjecture revisited: Finiteness of pointed families of polarized varieties (joint with Ruiran Sun and Kang Zuo) (arxiv)
   Submitted.
10. Rational points and ramified covers of products of two elliptic curves (arxiv, journal)
    Acta Arith. 198 (2021), no. 3, 275–287.
11. Urata's theorem in the logarithmic case and applications to integral points (joint with Aaron Levin) (arxiv, journal)
    Bull. London Math. Soc., 54: 1772-1790.
12. Finiteness properties of pseudo-hyperbolic varieties (joint with Junyi Xie) (arxiv, journal)
    International Mathematics Research Notices, Volume 2022, Issue 3, February 2022, 1601-1643
13. Integral points on algebraic subvarieties of period domains: from number fields to finitely generated fields (joint with Daniel Litt) (arxiv)
    Submitted.
14. Boundedness in families with applications to arithmetic hyperbolicity (joint with Raymond van Bommel and Ljudmila Kamenova) (arxiv)
    Submitted.
15. Effective estimates for the degrees of special maximal subvarieties (joint with Christopher Daw and Lars Kühne) (arxiv, journal)
    Selecta. Math. New Ser. 26, 2 (2020)
16. Arithmetic hyperbolicity: automorphisms and persistence (arxiv, journal)
    Math. Ann. 381, 439–457 (2021)
17. Non-archimedean hyperbolicity and applications (joint with Alberto Vezzani) (arxiv, journal)
    Journal für die reine und angewandte Mathematik (Crelles Journal), vol. 2021, no. 778, 2021, pp. 1-29
18. Arithmetic hyperbolicity and a stacky Chevalley-Weil theorem (joint with Daniel Loughran) (arxiv , journal)
    J. London Math. Soc. (2) 103 (2021) 846-869..
19. Demailly's notion of algebraic hyperbolicity: geometricity, boundedness, moduli of maps (joint with Ljudmila Kamenova) (arxiv,  journal)
    Math. Zeitschrift, volume 296, pages 1645-1672 (2020)
20. Algebraicity of analytic maps to a hyperbolic variety (joint with Robert A. Kucharczyk) (arxiv, journal)
    Math. Nachrichten, 293 (2020), no. 8 (August).
21. Horospherical stacks (joint with Kevin Langlois and Ronan Terpereau) (arxiv, journal)
    Münster J. of Math. Volume 12 (2019), p. 1-29.
22. The Belyi degree of a curve is computable (joint with John Voight) (arxiv, journal)
    Contemp. Math., 2019, 722, p. 43-57.
23. Invariants of smooth Fano varieties in families (joint with Frank Gounelas) (arxiv, journal)
    Moscow Mathematical Journal, Volume 18, Issue 2 (2018), p. 305-319.
24. Good reduction of Fano threefolds and sextic surfaces. (joint with Daniel Loughran) (arxiv, journal)
    Annali della Scuola Normale Superiore di Pisa, Classe di Scienze, Serie V, Vol. XVIII, Fasc. 2 (2018), 509-535 
25. Bounding heights uniformly in families of hyperbolic varieties. (joint with Ken Ascher) (arxiv, journal)
    New York J. Math. 23 (2017), 1791-1808
26. Effectively computing integral points on the moduli of smooth quartic curves. (arxiv, journal)
    The Quarterly Journal of Mathematics, Volume 68, Issue 2, 1 June 2017, Pages 345–358
27. The moduli of smooth hypersurfaces with level structure. (joint with Daniel Loughran) (arxiv, journal)
    Manuscripta Math. 154 (2017), no. 1-2, 13–22.
28. Complete intersections: Moduli, Torelli, and good reduction. (joint with Daniel Loughran) (arxiv, journal)
    Math. Ann. 368 (2017), no. 3-4, 1191–1225.
29. Belyi's theorem for complete intersections of general type. (arxiv, journal)
    Michigan Math. J. Volume 66, Issue 1 (2017), 85-97.
30. An effective Arakelov-theoretic version of the hyperbolic isogeny theorem. (arxiv, journal)
    Math. Proc. Cambridge Phil. Soc., (2016) Vol. 160, Issue 03, 463-476.
31. Good reduction of algebraic groups and flag varieties. (joint with Daniel Loughran) (arxiv, journal )
    Archiv der Math., (2015) Vol. 104, Issue 2,  133-143.
32. Néron models and the arithmetic Shafarevich conjecture for certain canonically polarized varieties.  (journal)
    Bull. London Math. Soc., (2015) 47 (1).
33. Szpiro's small points conjecture for cyclic covers. (joint with Rafael von Kaenel) (arxiv, journal)
    Documenta Math., 19 (2014) 1085-1103.
34. Polynomial bounds for Arakelov invariants of Belyi curves, with an appendix by Peter Bruin. (arxiv, journal)
    Algebra and Number Theory, Vol. 8 (2014), No. 1, 89–140.

 

Lecture notes

1. The Lang-Vojta conjectures on projective pseudo-hyperbolic varieties. (arxiv, journal)
   One of four chapters in "Arithmetic Geometry of Logarithmic Pairs and Hyperbolicity of Moduli Spaces" published by  CRM Short Courses Springer. 

Videos

1. Talk at Banff  "Geometry via Arithmetic" "Rational points on ramified covers of abelian varieties" on [2]
2. Talk at Western Algebra Geometry ONline "Albanese maps and fundamental groups of varieties with many rational points over function fields" on [3]
3. Talk at MSRI "Finiteness properties of hyperbolic varieties" on [8], [12], and [15]
4. Talk at CIRM Luminy "Arithmetic and algebraic hyperbolicity" on [8], [12], and [15]

 

Teaching/Lehre

1. Vorlesung "Zahlentheorie". Winter 2021 (Mainz)
2. Seminar "Topics in Commutative Algebra". Summer 2021 (Mainz)
3. Vorlesung "Analytische Zahlentheorie". Summer 2021 (Mainz)
4. Vorlesung "Algebraic Geometry (Algebraische Geometrie)". Winter 2020. (TU Chemnitz)
5. Vorlesung "Representation theory (Darstellungstheorie)". Winter 2020. (TU Chemnitz)
6. Vorlesung "Hyperbolische Geometrie". Summer 2020. (TU Chemnitz).
7. Vorlesung "Algebra". Summer 2020. (TU Chemnitz)
8. Vorlesung "Algebraische Zahlentheorie, II". Winter 2019. (Mainz)
9. Vorlesung "Elementarmathematik (BEd.)". Winter 2019. (Mainz)
10. Vorlesung "Algebraische Zahlentheorie, I". Summer 2019. (Mainz)
11. Vorlesung "Elementarmathematik (BEd.)". Summer 2019. (Mainz)
12. Vorlesung "Elementarmathematik (BEd.)", Winter 2018. (Mainz)
13. Vorlesung "Lin. Algebra und Geometrie II (BSc)", Winter 2018. (Mainz)
14. Seminar "Diophantine Approximation and Analytic Number Theory". Summer 2018. (Mainz)
15. Vorlesung "Algebra 2", Summer 2017. (Mainz)
16. Vorlesung "Lin. Algebra und Geometrie II (BSc)", Winter 2016. (Mainz)
17. Vorlesung "Elliptische Kurven II", Winter 2016. (Mainz)
18. Vorlesung "Elliptische Kurven I", Summer 2016. (Mainz)
19. Vorlesung "Algebraische Geometrie II", Winter 2015. (Mainz)
20. Vorlesung/Course "Elliptic curves, complex multiplication, modular curves",  together with Stefan Müller-Stach Winter 2014. (Mainz)
21. Übungsleiter  "Lineare Algebra und Geometrie II". Teacher: Theo de Jong. Winter 2014. (Mainz)
22. Übungsleiter  "Algebraische Kurven und Riemannsche Flächen". Teacher: Duco van Straten. Summer 2014. (Mainz)
23. Mitarbeiter für "Zahlentheorie". Teacher: Manuel Blickle. Winter 2013. (Mainz)

Ph.D. Students

1. Philipp Licht, 2016-2022. Homepage
2. Ruiran Sun, 2017-2021. Homepage
3. Cedric Luger, 2021-present. Homepage

 

Ph.D. Thesis

• Arakelov invariants of Belyi curves. Ph.D. thesis (Leiden University and University of Paris-Sud 11)
• Stellingen. These are the "Propositions".

Seminars/Workgroups/Groupes de Travail

• Moduli of curves and the theory of algebraic stacks, University of Mainz, Winter 2021.
• The Shafarevich conjecture for hypersurfaces in abelian varieties. Online, Winter 2020.
• Rational points on varieties. University of Mainz, Winter 2019.
• Workshop on Galois representation, Integral points, Unlikely intersections. University of Mainz. Summer 2019. 
• Algebraic properties of hyperbolic varieties. University of Mainz. Winter 2018.
• Talks on Hyperbolicity. University of Mainz. Summer 2017
• The Mainzer arXiv seminar. University of Mainz. Summer 2017.
• Darmstadt-Frankfurt-Mainz meetings. Winter 2016.
• Derived categories in algebraic geometry. University of Mainz. Winter 2016.
• Arakelov invariants, Belyi's theorem, and Szpiro's small points conjecture. Chalmers University Gothenburg. April 2016.
• Fano varieties. MPI Bonn and University of Mainz. Wintersemester 2015-2016.
• Torelli theorems and Hodge theory. University of Mainz. Summersemester 2014-2015
  
• Abelian varieties.  University of Mainz. Wintersemester 2014-2015
• Neron models of smooth proper varieties (after Artin, Bosch, Lütkebohmert, Neron, Raynaud, and Liu & Tong). University of Mainz. Summersemester 2013-2014
• The Shafarevich conjecture (after Arakelov, Campana, Kovacs, Kebekus, Parshin, Patakfalvi, Viehweg, Zuo,...). Leiden University, Summersemester 2012-2013 

Summer school 2018: International summer school on arithmetic geometry

• International summer school on arithmetic geometry. University of Salerno. 10-09-2018 until 14-10-2018 

This summer school is organized by Davide Cesare Veniani, Dino Festi and myself with the help of SFB/TRR 45 Bonn-Essen-Mainz and will take place in Salerno (Italy) from September 10th until September 14th, 2018.

Autumn School 2017: Topics in arithmetic and algebraic geometry

• Topics in arithmetic and algebraic geometry. University of Mainz. 9-10-2017 until 13-10-2017

This autumn school is organized by Davide Cesare Veniani, Dino Festi and myself with the help of SFB/TRR 45 Bonn-Essen-Mainz and took place in Mainz from October 9th until October 13th, 2017.

Summer School 2015: Algebraic Stacks

• Algebraic stacks and related topics. University of Mainz. 31-08-2015 until 04-09-2015.
  

This summer school was organized by Ronan Terpereau and myself with the help of SFB/TRR 45 Bonn-Essen-Mainz and took place in Mainz from August 31st until September 4th, 2015. The website contains live-teXed notes for most of the lectures.

 

 

Links

SFB/TRR45 Kolloquium

Mathoverflow

Robert Wilms

Philipp Licht