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Research interests 
My research interests mainly concern the automation of asymptotic
calculus and complex analysis, as well as fast arithmetic. Besides,
I am the main developer of the software systems GNU
TeXmacs and
My PhD. thesis and the book Transseries
and Real Differential Algebra are devoted to the theory of
transseries. The main results concern the asymptotic resolution of
differential equations, several closure theorems and embedding
theorems into Hardy fields. This work has been further extended in
collaboration with Matthias Another main research topic of mine is the automation of complex analysis and computations with special functions or more general solutions to differential equations. On the one hand, this leads to interesting theoretical questions about computability, zerotesting, singularities, etc. On the other hand, this requires the development and implementation of fast, certified and numerically stable algorithms for multiprecision computations.
The development of fast algorithms for basic mathematical operations
has evolved into one of my research topics on its own. In
collaboration with David 
GNU TeXmacs 
GNU TeXmacs is a free wysiwyw (what you see is what you want) editing platform with special features for scientists. The software aims to provide a unified and user friendly framework for editing structured documents with different types of content (text, graphics, mathematics, interactive content, etc.). The rendering engine uses highquality typesetting algorithms so as to produce professionally looking documents, which can either be printed out or presented from a laptop. The software includes a text editor with support for mathematical formulas, a small technical picture editor and a tool for making presentations from a laptop. Moreover, TeXmacs can be used as an interface for many external systems for computer algebra, numerical analysis, statistics, etc. New presentation styles can be written by the user and new features can be added to the editor using the Scheme extension language. A native spreadsheet and tools for collaborative authoring are planned for later. 


Distinctions and awards 
N.G. de Bruijn Medal 2022 for the joint
paper Integer multiplication in time
with David
Best 2020 paper award by the Journal of Complexity for
the joint paper Directed evaluation with
Grégoire
Invited lecture “On Numbers, Germs, and
Transseries” at the ICM 2018 about my joint
work with Matthias
Best 2016 paper award by the Journal of Complexity for
the joint paper Even faster integer multiplication with
David
ISSAC 2014 distinguished software presentation award with
Grégoire