Junior Prof. Dr. Ariyan Javanpeykar

Foto Tatihou

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.

Papers

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.

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

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

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

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

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

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

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

Good reduction of Fano threefolds and sextic surfaces. (joint work with Daniel Loughran) (arxiv)
Annali della Scuola Normale Superiore di Pisa, Classe di Scienze, to appear.

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

Bounding heights uniformly in families of hyperbolic varieties. (joint work with Ken Ascher) (arxiv)
Submitted.

Horospherical stacks (joint work with Kevin Langlois and Ronan Terpereau) (arxiv)
Submitted. 

Invariants of smooth Fano varieties in families (joint with Frank Gounelas) (arxiv)
Submitted.

Period maps and the arithmetic of stacks (joint with Daniel Loughran)
In preparation

 

Teaching/Lehre

  1. Vorlesung "Algebra 2", Summer 2017.
  2. Vorlesung "Lin. Algebra und Geometrie II (BSc)", Winter 2016-2017.
  3. Vorlesung "Elliptische Kurven II", Winter 2016-2017.
  4. Vorlesung "Elliptische Kurven I", Summer 2015-2016.
  5. Vorlesung "Algebraische Geometrie II", Winter 2015-2016.
  6. Vorlesung/Course "Elliptic curves, complex multiplication, modular curves",  together with Stefan Müller-Stach Winter 2014-2015.
  7. Übungsleiter  "Lineare Algebra und Geometrie II". Teacher: Theo de Jong. Winter 2014-2015.
  8. Übungsleiter  "Algebraische Kurven und Riemannsche Flächen". Teacher: Duco van Straten. Summer 2013-2014
  9. Mitarbeiter für "Zahlentheorie". Teacher: Manuel Blickle. Winter 2013-2014

Ph.D. Thesis

Seminars/Workgroups/Groupes de Travail

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 will take 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