Publications, Lecture Notes, Survey papers

Papers

1. Hilbert irreducibility for abelian varieties over function fields of characteristic zero (arxiv)
   Submitted

2. Symmetric products and puncturing Campana-special varieties (joint with Finn Bartsch and Aaron Levin). (arxiv)
   Proc. Lond. Math. Soc. (3) 131 (2025), no. 6, Paper No. e70108.

3. The Weakly Special Conjecture contradicts orbifold Mordell, and hence the abc conjecture (joint with Finn Bartsch, Frédéric Campana, and Olivier Wittenberg). (arxiv)
   J. Eur. Math. Soc. (JEMS), to appear.

4. Weakly-special threefolds and non-density of rational points (joint with Finn Bartsch and Erwan Rousseau). (arxiv)
   J. Lond. Math. Soc. (2) 112 (2025), no. 5, Paper No. e70348.

5. Finiteness of pointed maps to moduli spaces of polarized varieties (joint with Steven Lu, Ruiran Sun, and Kang Zuo). (arxiv)
   Submitted.

6. Kobayashi-Ochiai's finiteness theorem for orbifold pairs of general type (joint with Finn Bartsch). (arxiv, journal)
   Journal of the Institute of Mathematics of Jussieu,  2024; 23(6):2713-2732.  

7. The monodromy of families of subvarieties on abelian varieties (joint with Thomas Krämer, Christian Lehn, and Marco Maculan). (arxiv)
   Duke Math. J. 174 (2025), no. 6, 1045-1149.

8. Smooth hypersurfaces in abelian varieties over arithmetic rings (joint with Siddharth Mathur) (arxiv, journal)
   Forum of Mathematics, Sigma, 10, E97.

9. Hilbert irreducibility for varieties with a nef tangent bundle (arxiv).
   J. Ramanujan Math. Soc. 39, No.1 (2024) 33-38.

10. Finiteness of non-constant maps over number fields (arxiv, journal).
    Math. Res. Lett. 30 (2023), no. 5, 1521–1534.

11. Algebraic intermediate hyperbolicities (joint with Antoine Etesse and Erwan Rousseau) (arxiv, journal)
    Doc. Math. 27, 2469-2490 (2022)

12. On the distribution of rational points on ramified covers of abelian varieties (previously: Hilbert's irreducibility theorem for abelian varieties) (joint with Pietro Corvaja, Julian Lawrence Demeio, Davide Lombardo, and Umberto Zannier) (arxiv, journal)
    Compositio Math. 158 (2022), 2109-2155.

13. Albanese maps and fundamental groups of varieties with many rational points over function fields (joint with Erwan Rousseau) (arxiv, journal)
    Int. Math. Res. Not. IMRN 2022, no. 24, 19354-19398.

14. Good reduction and cyclic covers (joint with Daniel Loughran and Siddharth Mathur) (arxiv, journal)
    J. Inst. Math. Jussieu 23 (2024), no. 1, 463-494.

15. The Shafarevich conjecture revisited: Finiteness of pointed families of polarized varieties (joint with Ruiran Sun and Kang Zuo) (arxiv)
    Submitted.

16. Rational points and ramified covers of products of two elliptic curves (arxiv, journal)
    Acta Arith. 198 (2021), no. 3, 275–287.

17. 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.

18. Finiteness properties of pseudo-hyperbolic varieties (joint with Junyi Xie) (arxiv, journal)
    International Mathematics Research Notices, Volume 2022, Issue 3, February 2022, 1601-1643

19. Integral points on algebraic subvarieties of period domains: from number fields to finitely generated fields (joint with Daniel Litt) (arxiv,journal)
    Manuscripta Math. 173 (2024), no. 1-2, 23-44.

20. Boundedness in families with applications to arithmetic hyperbolicity (joint with Raymond van Bommel and Ljudmila Kamenova) (arxiv, journal)
    J. London Math. Soc., 109: e12847.
    Erratum: Click here.

21. 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)

22. Arithmetic hyperbolicity: automorphisms and persistence (arxiv, journal)
    Math. Ann. 381, 439–457 (2021)

23. 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

24. Arithmetic hyperbolicity and a stacky Chevalley-Weil theorem (joint with Daniel Loughran) (arxiv , journal)
    J. London Math. Soc. (2) 103 (2021) 846-869.

25. 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)
    Erratum: Click here.

26. Algebraicity of analytic maps to a hyperbolic variety (joint with Robert A. Kucharczyk) (arxiv (not updated yet), journal)
    Math. Nachrichten, 293 (2020), no. 8 (August).

27. Horospherical stacks (joint with Kevin Langlois and Ronan Terpereau) (arxiv, journal)
    Münster J. of Math. Volume 12 (2019), p. 1-29.

28. The Belyi degree of a curve is computable (joint with John Voight) (arxiv, journal)
    Contemp. Math., 2019, 722, p. 43-57.

29. Invariants of smooth Fano varieties in families (joint with Frank Gounelas) (arxiv, journal)
    Moscow Mathematical Journal, Volume 18, Issue 2 (2018), p. 305-319.

30. 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 

31. Bounding heights uniformly in families of hyperbolic varieties. (joint with Kenneth Ascher) (arxiv, journal)
    New York J. Math. 23 (2017), 1791-1808

32. 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

33. The moduli of smooth hypersurfaces with level structure. (joint with Daniel Loughran) (arxiv, journal)
    Manuscripta Math. 154 (2017), no. 1-2, 13–22.

34. Complete intersections: Moduli, Torelli, and good reduction. (joint with Daniel Loughran) (arxiv, journal)
    Math. Ann. 368 (2017), no. 3-4, 1191–1225.

35. Belyi's theorem for complete intersections of general type. (arxiv, journal)
    Michigan Math. J. Volume 66, Issue 1 (2017), 85-97.

36. An effective Arakelov-theoretic version of the hyperbolic isogeny theorem. (arxiv, journal)
    Math. Proc. Cambridge Phil. Soc., (2016) Vol. 160, Issue 03, 463-476.

37. Good reduction of algebraic groups and flag varieties. (joint with Daniel Loughran) (arxiv, journal )
    Archiv der Math., (2015) Vol. 104, Issue 2,  133-143.

38. Néron models and the arithmetic Shafarevich conjecture for certain canonically polarized varieties.  (journal)
    Bull. London Math. Soc., (2015) 47 (1).

39. Szpiro's small points conjecture for cyclic covers. (joint with Rafael von Kaenel) (arxiv, journal)
    Documenta Math., 19 (2014) 1085-1103.

40. 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, Expository writing, Survey papers.

1. Parshin's method and the geometric Bombieri-Lang conjecture. (joint with Finn Bartsch) (arxiv, journal)
   Indag. Math. (N.S.) 37 (2026), no. 1, 271–280. Special Issue dedicated to the memory of Jacob Murre.  

2. 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. 

3. Hilbert properties of varieties (joint with Arno Fehm) (arxiv)
   Submitted.