Ariyan Javanpeykar

ALGANT Ph.D. student at Universiteit Leiden and at Université Paris-Sud 11 in Orsay. My supervisors are Jean-Benoit Bost, Bas Edixhoven, and Robin de Jong.

My research focuses on applications of Arakelov theory to problems in arithmetic geometry.

Keywords and themes are: Arakelov's inequality, Arakelov-Green functions, arithmetic surfaces, Arakelov invariants, covers of varieties, Arakelov intersection theory, Belyi degree, Shafarevich conjecture, computational aspects of etale cohomology.

Contact information:

Telephone: +31 71 527 7119
E-mail: ajavanp at math dot leidenuniv dot nl
Address: Snellius building, office 219, Postbus 9521, 2300 RA Leiden

Please do not hesitate to contact me for any comments, remarks or questions.



Publications

Polynomial bounds for Arakelov invariants of Belyi curves [with an appendix by Peter Bruin]. Algebra and Number Theory, to appear

Preprints

Szpiro's small points conjecture for cyclic covers [joint with Rafael von Kanel]. Submitted
Arakelov's inequality and heights of covers of varieties. Preprint (available upon request).

Ph.D. Thesis | Proefschrift (June 2013)

Ph.D. Thesis Arakelov invariants of Belyi curves (PDF)
Promotor Bas Edixhoven
Promotor Jean-Benoit Bost
Copromotor Robin de Jong
Stellingen Propositions in Dutch

Master Thesis (May 2010)

Master thesis written under the supervision of Professor Jaap Murre: The Grothendieck-Riemann-Roch theorem

Bachelor Thesis (June 2008)

Bachelor thesis written under the supervision of Franck Doray and Koenraad Schalm: Representation, homotopy and gauge theory for SU_2(R) with a view towards Witten's global SU(2) anomaly

Current seminars

Talks

Most of the notes below were written down for lectures given at Ph.D. seminars. It is well known that such notes often contain inaccuracies.

Arakelov invariants and the Belyi degree notes REGA Seminar October 10, 2012, Institut Henri Poincare, Paris
Arakelov invariants of curves notes Seminaire d'algebre et theorie de nombres September 27, 2012, Besancon, France
Bounds for Arakelov invariants of Belyi curves notes Arithmetische Geometrie und Zahlentheorie May 16, 2012, Hamburg University, Germany
Introduction to Grothendieck's generalized trace formula notes (in progress) Seminar on Etale cohomology 2011 May 31, 2011 Leiden University
Heights of covers of arithmetic surfaces with fixed branch locus notes Heights in Diophantine and Arakelov Geometry, Dynamical Systems and Computer Algebra April 29, 2011 Tossa de Mar
Introduction to heights notes Topics in Arithmetic Geometry 2010-2011 April 18, 2011 Leiden University
Geometric points, etale neighborhoods, stalks, direct images and inverse images notes Seminar on Etale cohomology 2011 April 5, 2011 Leiden University
Locally ringed spaces and affine schemes notes Topics in Arithmetic Geometry 2010-2011 February 28, 2011 Leiden University
The generalized Lefschetz trace formula notes (in progress) L'hypothese de Riemann d'apres Deligne November 25, 2010 Université Paris 13
The Grothendieck-Riemann-Roch theorem and heights for covers of surfaces with fixed branch locus II notes Seminar Mathjeunes October 30, 2010 Université Paris-Sud 11
The Grothendieck-Riemann-Roch theorem and heights for covers of surfaces with fixed branch locus I notes Seminar Mathjeunes October 23, 2010 Université Paris-Sud 11
Short talk on master's thesis sheets ALGANT graduation ceremony 2010 July, 2010 Université Bordeaux

Teaching

Teaching assistant for a course on Algebraic topology (taught by Robin de Jong) Introduction to Algebraic Topology Fall 2011, Universiteit van Leiden
Teaching assistant for Linear Algebra 2 (taught by Bart de Smit) Linear Algebra 2 Fall 2011, Universiteit van Leiden
Teaching assistant for the Mastermath course (taught by Bas Edixhoven) Algebraic Geometry Spring 2011, Universiteit van Amsterdam
Teaching assistant for Analyse 2 (taught by Frank den Hollander and Vivi Rottschaffer) Studiegids Spring 2008, Universiteit van Leiden

Notes

The Atiyah-Singer index theorem (Spring 2009) Notes on a course by Jean-Michel Bismut (will be finished some day).
The Atiyah-Janich theorem in Noncommutative Geometry (Spring 2009) notes

Links

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