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).

Translations: fr