# Research

**If you don't know anything about combinatorics, you can watch this video where I give an example of a nice result to present my research (French with Engligh subtitles).**

My research field is **algebraic combinatorics**: I study algebraic structures such
as Hopf algebras and partial orders applied on combinatorial objects. I am especially
interested in the links between **Hopf algebras**, **partial orders**, and **polytopes**.
My favorite objects are permutations and binary trees along with all their associated
structures: the Tamari lattice,
the weak order, [the Permutohedron]((https://en.wikipedia.org/wiki/Permutohedron),
the Associahedron, etc.

The image on the right is a 3D-printed Permutreehedron: its vertices are counted by some objects, interpolating in-between permutations and binary trees (18 in the example).

Software development is an important part of my research often based on
**computer exploration**. The idea is to model mathematical objects through code
to allow for experimentation on their properties.

I'm explaining this over here: Talk at Pycon 2015 -- short version Lightning talk, SciPy 2014 (30:20).

## Publications

All my papers are available on arXiv (with latex source), on Google Scholar, and on HAL. Habilitation à diriger des recherches Combinatorics of the Permutahedra, Associahedra, and Friends defended on October, 20 2023 at Paris-Saclay University [ arXiv ][ HAL ]

## Talks and Posters

You will find below my most recent presentations, you can also go through the full list or look by thematic. Please contact me if you need the latex source for any of the presentations.

## Conferences

I am listing here all the conferences and research schools which I either organize or where I give a major intervention / training.

## Projects

PAGCAP 2022 -- 2026 Beyond Permutahedra and Associahedra: Geometry, Combinatorics, Algebra, and Probability I am the coordinator of the PAGCAP project, an ANR -- FWF International Collaborative Research Project between France and Austria running from 2022 to 2026. It lies at the intersection of theoretical computer science and pure mathematics, aiming to …

Translations: fr