# Simon Abelard

## About me

Since January 2021, I am an engineer at Thales Group. This page is about my academic activities and does not reflect the position of the company.

From October 2019 to December 2020, I have been a postdoctoral researcher at LIX (Laboratoire d'Informatique de l'Ecole Polytechnique) and from September 2018 to September 2019 in the Symbolic Computation group at the University of Waterloo (Ontario).

From September 2015 to September 2018, I have been a Ph.D. student at Université de Lorraine, and a member in the LORIA's project-team CARAMBA, under the supervision of Pierrick Gaudry and Pierre-Jean Spaenlehauer. Meanwhile, I have also been a teaching assistant at Mines Nancy.

I defended my thesis on September 7, 2018. Here is a link to the manuscript and to the slides of the defense (both in English).** Errata:** in the RM case, the exponent in the complexity should be 9 instead of 8 (and the conjectured bound is then 7 instead of 6). This has been corrected in a more recent article published in the Journal of Complexity.

## Research interests

My goal is to design better algorithms to handle algebraic curves over finite fields, reaching better complexity bounds, providing efficient implementations, record computations and practical constructions.

To do so, the following areas of Mathematics and Computer Science are of particular interests to me:

- Computer Algebra
- Algorithmic Number Theory
- Commutative Algebra
- Algebraic Geometry

My work aims at solving algorithmic problems for a variety of applications in

- Cryptography
- Coding Theory
- Zero-Knowledge Proofs

## Contact me

E-mail: |
sabelard(at)protonmail.com |