Junior Prof. Dr. Ariyan Javanpeykar

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.

 

Papers

  1. Good reduction and cyclic covers (joint with Daniel Loughran and Siddharth Marthur) (arxiv)
    Submitted.
  2. The Shafarevich conjecture revisited: Finiteness of pointed families of polarized varieties (joint with Ruiran Sun and Kang Zuo) (arxiv)
    Submitted.
  3. Hilbert's irreducibility theorem for products of elliptic curves (arxiv).
    Submitted.
  4. Urata's theorem in the logarithmic case and applications to integral points (joint with Aaron Levin) (arxiv)
    Submitted
  5. Finiteness properties of pseudo-hyperbolic varieties (joint with Junyi Xie) (arxiv, journal)
    IMRN, to appear.
  6. Integral points on algebraic subvarieties of period domains: from number fields to finitely generated fields (joint with Daniel Litt) (arxiv)
    Submitted.
  7. Boundedness in families with applications to arithmetic hyperbolicity (joint with Raymond van Bommel and Ljudmila Kamenova) (arxiv)
    Submitted.
  8. 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)
  9. Arithmetic hyperbolicity: automorphisms and persistence (arxiv)
    Submitted.
  10. Non-archimedean hyperbolicity and applications (joint with Alberto Vezzani) (arxiv)
    Submitted.
  11. Arithmetic hyperbolicity and a stacky Chevalley-Weil theorem (joint with Daniel Loughran) (arxiv)
    Journal of the London Math. Society, to appear.
  12. Demailly's notion of algebraic hyperbolicity: geometricity, boundedness, moduli of maps (joint with Ljudmila Kamenova) (arxiv,  journal)
    Math. Zeitschrift, to appear.
  13. Algebraicity of analytic maps to a hyperbolic variety (joint with Robert A. Kucharczyk) (arxiv, journal)
    Math. Nachrichten, 293 (2020), no. 8 (August).
  14. Horospherical stacks (joint with Kevin Langlois and Ronan Terpereau) (arxiv, journal)
    Münster J. of Math. Volume 12 (2019), p. 1-29.
  15. The Belyi degree of a curve is computable (joint with John Voight) (arxiv, journal)
    Contemp. Math., 2019, 722, p. 43-57.
  16. Invariants of smooth Fano varieties in families (joint with Frank Gounelas) (arxiv, journal)
    Moscow Mathematical Journal, Volume 18, Issue 2 (2018), p. 305-319.
  17. 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 
  18. Bounding heights uniformly in families of hyperbolic varieties. (joint with Ken Ascher) (arxiv, journal)
    New York J. Math. 23 (2017), 1791-1808
  19. 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
  20. The moduli of smooth hypersurfaces with level structure. (joint with Daniel Loughran) (arxiv, journal)
    Manuscripta Math. 154 (2017), no. 1-2, 13–22.
  21. Complete intersections: Moduli, Torelli, and good reduction. (joint with Daniel Loughran) (arxiv, journal)
    Math. Ann. 368 (2017), no. 3-4, 1191–1225.
  22. Belyi's theorem for complete intersections of general type. (arxiv, journal)
    Michigan Math. J. Volume 66, Issue 1 (2017), 85-97.
  23. An effective Arakelov-theoretic version of the hyperbolic isogeny theorem. (arxiv, journal)
    Math. Proc. Cambridge Phil. Soc., (2016) Vol. 160, Issue 03, 463-476.
  24. Good reduction of algebraic groups and flag varieties. (joint with Daniel Loughran) (arxiv, journal )
    Archiv der Math., (2015) Vol. 104, Issue 2,  133-143.
  25. Néron models and the arithmetic Shafarevich conjecture for certain canonically polarized varieties.  (journal)
    Bull. London Math. Soc., (2015) 47 (1).
  26. Szpiro's small points conjecture for cyclic covers. (joint with Rafael von Kaenel) (arxiv, journal)
    Documenta Math., 19 (2014) 1085-1103.
  27. 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)
    CRM Short Courses Springer, to appear. 

Videos

  1. Talk at Western Algebra Geometry ONline "Albanese maps and fundamental groups of varieties with many rational points over function fields"
  2. Talk at MSRI "Finiteness properties of hyperbolic varieties"
  3. Talk at CIRM Luminy "Arithmetic and algebraic hyperbolicity"

 

Teaching/Lehre

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

Ph.D. Thesis

Seminars/Workgroups/Groupes de Travail

Summer school 2018: International summer school on arithmetic geometry

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

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

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