Richard Griffon

Postdoc in Number Theory

Id Photo
Universität Basel - Departement Mathematik und Informatik
Spiegelgasse 1
CH-4051 Basel, Switzerland
E-mail : richard.griffon /at/ unibas.ch
Office : 3.003


Since September 2018, I am a postdoctoral researcher at the University of Basel (Switzerland), in the research group of Pierre Le Boudec. Before that, I was a postdoc at Leiden University (the Netherlands) for two years.

I obtained my PhD degree at Université Paris Diderot in July 2016, working under the supervision of Marc Hindry.


Research

My main field of research is the arithmetic of elliptic curves over global fields. I mostly study them over function fields in positive characteristic, and I usually take an analytic approach (by using their $L$-function). The main topic of my research is the asymptotic behaviour of the so-called Brauer-Siegel ratio of elliptic curves: this invariant is related to the difficulty of computing their Mordell-Weil groups. It can be controlled by estimating the size of the special values of their $L$-functions. In some cases, one can prove that the Brauer-Siegel ratio has a limit. In all known cases, this limit is $1$ (i.e. the Mordell-Weil groups of the elliptic curves are indeed complicated to compute).
I have also worked with surfaces over a finite field: for some families, I have proved very precise bounds on some of their geometric invariants.

Keywords: Elliptic curves over global fields, L-functions of elliptic curves (and explicit computations of those), Birch and Swinnerton-Dyer conjecture, Estimates of special values of L-functions at s=1, Surfaces over finite fields, Estimates of their special value at s=1, Artin-Tate conjecture, Brauer-Siegel theorem and analogues.

Articles and preprints

Find my papers on arXiv, ORCID, MathSciNet.

Thesis

I did my PhD thesis under the supervision of Marc Hindry at Université Paris Diderot. My defence took place in July 2016. Here is the introduction (in English and in French) and the full text (in French).

Others


Teaching & Supervision

Courses taught

Students supervised


Last updated : November 2019