# Nicolas Mascot

## Dr Nicolas MascotResearch Fellow |

[Version française] - [Versión española] - [中文]

**Teaching responsibilities 2016/17:**

Term 2: MA3A6 Algebraic Number Theory (jointly with Aurel Page).

The materials for this course (lecture notes, exercise sheets...) are on this page.

**Research**

- Companion forms and explicit computation of PGL
_{2}number fields with very little ramification

arXiv preprint 1611.01464, November 2016. - Modular Galois representation data available for download

These data were computed and certified thanks to the algorithms descrbed in the two articles below. - Certified tables of modular Galois representations (To appear in Math. Comp. )

This article presents tables of modular Galois representations which were computed using the algorithm presented in the previous article, and shows how these computations can be formally certified. - Computing modular Galois representations (published in Rendiconti del Circolo Matematico di Palermo, Volume 62, No 3, December 2013)

This article describes how to explicitly compute modular Galois representations associated with a modular newform, and studies the related problem of computing the coefficients of this newform modulo a small prime. - My PhD thesis, Computing modular Galois representations

**A few old documents (in French !)**

- The Jacobian variety of a compact Riemann surface

These are the slides of a talk I gave in Bordeaux for the TNT days, and extended for the Λ seminar. It studies the periods of a connected compact Riemann surface, and then states and proves the Abel-Jacobi theorem. - Khinchin's constant

These are the slides of a talk I gave in Bordeaux for the TNT days. It presents Khinchin's constant, an amusing phenomenon in ergodic number theory. - An introduction to the Chabauty and Coleman method

This is the text of a talk I gave for my magistère at the École Normale Supérieure de Paris. It presents a geometric method to solve certain diophantine equations, starting form a rather low level. Its content was largely inspired by William McCallum's and Bjorn Poonen's article. - My Master's degree dissertation

It was supervised by Boas Erez, and focuses on algebraic varieties over finite fields and their Weil-étale cohomology. A few minor mistakes are still present, I'm afraid ! - Theta functions

This short dissertation, which was supervised by Laurent Clozel, focuses on theta functions attached to lattices as modular forms. - My Maîtrise dissertation

It is joint work with my fellow student Sylvain Arguillère, under Joël Merker's supervision. It deals with the computation of Lie symmetries of systems of PDEs and on the classification of local actions of Lie groups. - "Colles" questions

Here are the "colles" (oral examinations) questions I gave to Bernard Randé's MP*3 students at the lycée Louis le Grand, in 2008/09 and the beginning of 2009/10.