I am a post-doc of the ANR IZES at the SymPA team of the Laboratoire Amiénois de Mathématique Fondamentale et Appliquée (LAMFA) at Université de Picardie Jules-Verne.

I was previously a PhD student supervised by Nathalie Aubrun. You can find the thesis manuscript here.

Research interests

I am interested in symbolic dynamics, combinatorial and geometric group theory, computability theory, self-avoiding walks and computational complexity. My research focuses on the connections between symbolic dynamics, group theory, and computability theory. In particular, to understand the behavioral dichotomy that exists between subshifts defined over \(\mathbb{Z}\) and \(\mathbb{Z}^d\) for \(d\geq 2\), evidenced by many results on their computational and dynamical behavior. The aim of my research so far has been to determine which underlying properties of these groups are responsible for this dichotomy. This research has followed two main lines:

1. Dynamical properties of \(G\)-shifts

   The goal is to understand how different group properties constrain the dynamical properties of subshifts and vice versa. For instance, what are the conditions for a group to admit aperiodic subshifts of finite type? or subshifts defined by substitutions? How does the existence of such shifts affect the structure of the group?

2. Computability of tiling problems

   A tiling problem asks, given an input made up of a set of tiles and a set of local constraints on their placement, whether there exists a tiling of the group that satisfies a specific property. A classic example is the Domino Problem. I study how the underlying group's properties affect the tiling problems' decidability. One of the main goals is to characterize the class of groups where these problems are decidable, which is conjectured to be the class of virtually free groups.

Where to find me?

Bureau C103, UFR des Sciences, Université de Picardie Jules-Verne, 33 Rue St Leu 80000 Amiens