Version Française

I started my PhD in september 2017 under the supervision of Bernard Leclerc. My PhD subject is "Cluster algebra associated to open Richardson varieties : an algorithm to compute initial seeds". The goal of the PhD was to find an algorithm computing an initial seed for the cluster algebra structure on an open Richardson variety. In order to do so, we start from the category associated to the corresponding Schubert cell of the Richarson variety and, thank to a sequence a mutation, ending on a seed whom a subseed is a seed for the category associated to the open Richardson variety.

I defended my PhD these on March 10th 2021. I am currently writing an article about these results and working on prolongation of this work, notely the comparison between the seeds coming from my algorithm and those of Galashin and Lam and Serhiyenko, Shermann-Bennet and Williams.

You can find here a research statement summarizing my actual researches.

I developped a Sage implementation of these algorithms in order to test my conjectures. I am working on a rewriting of this implementation in order to make it more usable.

My PhD dissertation is available (in French) on Thèses En Ligne.

- Cluster algebras associated with open Richardson varieties: an algorithm to compute initial seeds, preprint, to be submitted soon to Algebras and Representation Theory
- SAGE library, implementation of my thesis algorithms (alpha version)
- My PhD thesis (in French)