• Home
• Research
• Teaching
• In french

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 Caen, in the south of France et I am teaching at the maths department. I am a searcher hosted at the Research Group in computer science, image and instrumentation of Caen.
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 tournament ! Students may follow the link lien for documents for lessons. If you wish to write to me to talk about mathematics or computer scinces, you can email me at: catoire_research@proton.me Mails won't be lost here !

You can download my english CV here.

Research works

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 mathematics 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

Publications

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

Published in a peer-reviewed journal

• Tridendriform structures
available in the journal SIGMA since 2023 on this link.

Online

• Tridendriform and dendriform Zeta Values from Schroeder trees (joint work with Pierre Clavier and Douglas Modesto da Fraga Candido);
In this work, we studied the links between shuffle relations in the theory of multiple zeta values and the free tridendriform and dendriform structures.
• The Cartier-Quillen-Milnor-Moore theorem in the Post-Hopf case;
This work states a analoguous of a known theorem in the richer structure of Post-Hopf algebras used in differential geometry.
• Effective approach of the tridendriform Schroeder tree algebra (joint work with Jean Fromentin).
It studied the free tridendriform structure from a computational and pratictal point of view and developed a Python library to perform complex computations in this algebra.

Ongoing projects

• a free tridendriform structure on the set of parking functions with Bérénice Delcroix-Oger at IMAG ;
• new generalization of some conjectures in the theory of MZVs involving trees with Pierre Clavier and Ku-Yu Fan;
• 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 computer science departement at Université de Caen for 192h this year. LAst year, I taught to students at the maths department of Université de Montpellier for 192h. I have taught to second year students at Polytech school of Montpellier, second year students in computer science degree and first year student of biology to help them with maths in their biology studies.s Two years ago, 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.