Pierre Catoire

Welcome on my web page, you can find fresh news about me here !

I am currently, a non-tenured searcher at université de Montpellier, in the south of France et I am teaching at the maths department. I am a searcher hosted atInstitut Montpeliérain Alexander Grothendieck .
I passed a PhD in mathematics at Université du Littoral Côte d'Opale in laboratoire de mathématiques pures et appliquées Joseph Liouville math lab.

I am also a chess player. So could have met me during one ! Students may follow the link lien for documents for lessons. If you wish to write to me to talk about mathematics, you can email me at: catoire_research@proton.me Mails won't be lost here !

You can download my english CV here.

Research works in mathematics

My research works are about combinatorial algebra at the intersection between mathematics and computer science
More precisely, I am working on combinatorial Hopf algebras and their applications in other fields of matheamtics like number theory, differential geometry, renormalisation theory in quantum physics or free probability theory.
Usually, I am trying to do mathematics with motivations or practical applications from other fields. This produces beautiful results. But, for sure, theory is also really important !

Research interests

My research work is about combinatorial Hopf algebras, Post-Hopf algebras, tridendriform algebras, operad theory and the study of some combinatorial objects likre trees, parking functions, words or matroids...
Moreover, I also enjoy to look some specific combinatorial issues. Currently, I want to spend some time to the study of the cycle double cover conjecture .

Publications

Here is a link to my PhD thesis (in french infortunately as I did not have time to type a translation)entitled "Algebraic context for combinatorial Hopf algebras applications". In this document, I am studying many different Hopf algebras appearing in other domains of mathematics:

the free tridendriform algebras described by Schroeder trees;
double bialgebra structure for matrices and matroids;
Post-Hopf algebras appearing in differential geometry.

Until now, I am detailling the list of documents available on ArXiV:

Published in a peer-reviewed journal

Tridendriform structures

lien

Online

Tridendriform and dendriform Zeta Values from Schroeder trees

(joint work with Pierre Clavier and Douglas Modesto da Fraga Candido).

The Cartier-Quillen-Milnor-Moore theorem in the Post-Hopf case.

Ongoing projects

I am now working on:

a free tridendriform structure on the set of parking functions with Bérénice Delcroix-Oger at IMAG .
practical computations in free tridendriform algebras with a computer. I am working with Jean Fromentin on this project at the maths laboratory of université du littoral côte d'opale.
on the algebraic notions in numerical integration and in the context of differential geometry with Léopold Trémant at laboratoire de mathématiques de Lens and Abrien Busnot-Laurent at IRMAR.
other subjects still opened in my thesis about Post-Hopf algebras and the double bialgebra structure for matroids..

Teaching

I am currently teaching at the maths departement at Université de Monptellier for 192h this year. Last year, I was teaching in a computer science department for 192h/year at IUT de Lens to student in first and second year. I have made many practical works files either with the help of Léopold Trémant. If you want to get those files (in french) go to the french webpage. During my PhD, I have taught 2 years for 64h/year two courses called:

"Maths2:algebra": logic, naive set theory, maps, injectivity, surjectivity, bijectivity, countable sets and relations.
"Maths6:arithmetic": euclidian division, modular arithmetic, introduction to group theory, Bezout and Gauss theorem, division euclidienne, arithmétique modulaire, une introduction à la théorie des groupes, théorème de Bézout et de Gauss, solving equations systems with moduli.

To summarize, I have mainly taught to students doing either computer science studies or maths studies in different courses like: arithmetic, basic programation, machine learning, analysis with series, arithmetic and cryptography, basic statistics and set theory.

J'ai enseigné à l'université du Littoral Côte d'Opale en 2023 et 2024 aux premières années de licence en mathématiques et informatique les deux cours suivants: