I obtained my PhD in June 2013 under the supervision of J.-B. Bost (Paris-Sud 11), Bas Edixhoven (Leiden), and Robin de Jong (Leiden). From July 2013 until November 2015 I was a post-doctoral fellow supported by the SFB/Transregio 45. Appointed as a (non tenure track) Junior Professor in Mainz and currently on leave for two semesters, as I will be at TU Chemnitz during the summer and winter semesters of 2020. I was positively evaluated as a Junior Professor in May 2018, and therefore hold the equivalent of a Habilitation. I am also a CNRS visiting researcher in July, August, and September of 2020 at Paris-Saclay.
My research is concerned with Arakelov theory, Belyi's theorem, Lang-Vojta's conjecture on rational points, Kobayashi's notion of hyperbolicity, Shimura varieties, period domains, non-archimedean hyperbolicity, and
dynamical systems in arithmetic geometry. In my work I employ algebraic stacks, Hodge theory, and arithmetic geometry. Below you will find a list of papers and three videos of some talks I gave on my research.
- Good reduction and cyclic covers (joint with Daniel Loughran and Siddharth Marthur) (arxiv)
- The Shafarevich conjecture revisited: Finiteness of pointed families of polarized varieties (joint with Ruiran Sun and Kang Zuo) (arxiv)
- Hilbert's irreducibility theorem for products of elliptic curves (arxiv).
- Urata's theorem in the logarithmic case and applications to integral points (joint with Aaron Levin) (arxiv)
- Finiteness properties of pseudo-hyperbolic varieties (joint with Junyi Xie) (arxiv, journal)
IMRN, to appear.
- Integral points on algebraic subvarieties of period domains: from number fields to finitely generated fields (joint with Daniel Litt) (arxiv)
- Boundedness in families with applications to arithmetic hyperbolicity (joint with Raymond van Bommel and Ljudmila Kamenova) (arxiv)
- 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)
- Arithmetic hyperbolicity: automorphisms and persistence (arxiv)
- Non-archimedean hyperbolicity and applications (joint with Alberto Vezzani) (arxiv)
- Arithmetic hyperbolicity and a stacky Chevalley-Weil theorem (joint with Daniel Loughran) (arxiv)
Journal of the London Math. Society, to appear.
- Demailly's notion of algebraic hyperbolicity: geometricity, boundedness, moduli of maps (joint with Ljudmila Kamenova) (arxiv, journal)
Math. Zeitschrift, to appear.
- Algebraicity of analytic maps to a hyperbolic variety (joint with Robert A. Kucharczyk) (arxiv, journal)
Math. Nachrichten, 293 (2020), no. 8 (August).
- Horospherical stacks (joint with Kevin Langlois and Ronan Terpereau) (arxiv, journal)
Münster J. of Math. Volume 12 (2019), p. 1-29.
- The Belyi degree of a curve is computable (joint with John Voight) (arxiv, journal)
Contemp. Math., 2019, 722, p. 43-57.
- Invariants of smooth Fano varieties in families (joint with Frank Gounelas) (arxiv, journal)
Moscow Mathematical Journal, Volume 18, Issue 2 (2018), p. 305-319.
- 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
- Bounding heights uniformly in families of hyperbolic varieties. (joint with Ken Ascher) (arxiv, journal)
New York J. Math. 23 (2017), 1791-1808
- 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
- The moduli of smooth hypersurfaces with level structure. (joint with Daniel Loughran) (arxiv, journal)
Manuscripta Math. 154 (2017), no. 1-2, 13–22.
- Complete intersections: Moduli, Torelli, and good reduction. (joint with Daniel Loughran) (arxiv, journal)
Math. Ann. 368 (2017), no. 3-4, 1191–1225.
- Belyi's theorem for complete intersections of general type. (arxiv, journal)
Michigan Math. J. Volume 66, Issue 1 (2017), 85-97.
- An effective Arakelov-theoretic version of the hyperbolic isogeny theorem. (arxiv, journal)
Math. Proc. Cambridge Phil. Soc., (2016) Vol. 160, Issue 03, 463-476.
- Good reduction of algebraic groups and flag varieties. (joint with Daniel Loughran) (arxiv, journal )
Archiv der Math., (2015) Vol. 104, Issue 2, 133-143.
- Néron models and the arithmetic Shafarevich conjecture for certain canonically polarized varieties. (journal)
Bull. London Math. Soc., (2015) 47 (1).
- Szpiro's small points conjecture for cyclic covers. (joint with Rafael von Kaenel) (arxiv, journal)
Documenta Math., 19 (2014) 1085-1103.
- 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.
- The Lang-Vojta conjectures on projective pseudo-hyperbolic varieties. (arxiv)
CRM Short Courses Springer, to appear.
- Talk at Western Algebra Geometry ONline "Albanese maps and fundamental groups of varieties with many rational points over function fields"
- Talk at MSRI "Finiteness properties of hyperbolic varieties"
- Talk at CIRM Luminy "Arithmetic and algebraic hyperbolicity"
- Vorlesung "Algebraic Geometry (Algebraische Geometrie)". Winter 2020. (TU Chemnitz)
- Vorlesung "Representation theory (Darstellungstheorie)". Winter 2020. (TU Chemnitz)
- Vorlesung "Hyperbolische Geometrie". Summer 2020. (TU Chemnitz).
- Vorlesung "Algebra". Summer 2020. (TU Chemnitz)
- Vorlesung "Algebraische Zahlentheorie, II". Winter 2019. (Mainz)
- Vorlesung "Elementarmathematik (BEd.)". Winter 2019. (Mainz)
- Vorlesung "Algebraische Zahlentheorie, I". Summer 2019. (Mainz)
- Vorlesung "Elementarmathematik (BEd.)". Summer 2019. (Mainz)
- Vorlesung "Elementarmathematik (BEd.)", Winter 2018. (Mainz)
- Vorlesung "Lin. Algebra und Geometrie II (BSc)", Winter 2018. (Mainz)
- Seminar "Diophantine Approximation and Analytic Number Theory". Summer 2018. (Mainz)
- Vorlesung "Algebra 2", Summer 2017. (Mainz)
- Vorlesung "Lin. Algebra und Geometrie II (BSc)", Winter 2016. (Mainz)
- Vorlesung "Elliptische Kurven II", Winter 2016. (Mainz)
- Vorlesung "Elliptische Kurven I", Summer 2016. (Mainz)
- Vorlesung "Algebraische Geometrie II", Winter 2015. (Mainz)
- Vorlesung/Course "Elliptic curves, complex multiplication, modular curves", together with Stefan Müller-Stach Winter 2014. (Mainz)
- Übungsleiter "Lineare Algebra und Geometrie II". Teacher: Theo de Jong. Winter 2014. (Mainz)
- Übungsleiter "Algebraische Kurven und Riemannsche Flächen". Teacher: Duco van Straten. Summer 2014. (Mainz)
- Mitarbeiter für "Zahlentheorie". Teacher: Manuel Blickle. Winter 2013. (Mainz)
- 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
- 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.