Short description. I am presently engaged in collaborative work on various pure and applied topics, with a significant focus on:

• the spectral theory of the Laplacian on manifolds and, recently, on graphs: multiplicity of eigenvalues, delocalization of eigenfunctions, etc. The beauty of this subject lies in its practical relevance to physics, potential applications in areas like quantum physics and community detection, and its intersection with different branches of mathematics, including partial differential equations, dynamical systems, and graph theory.
• problems in optimal transport related to the stability of the optimal transport map. This is surprisingly related to spectral theory and, more classically, to functional inequalities, as shown in a joint work with Quentin Mérigot. More generally, I am interested in understanding good and stable ways to map measures to other measures, in particular due to the importance of this problem in recent developments in machine learning.
• advancing our mathematical comprehension of Transformers and the self-attention mechanism. The mathematical tools we employ encompass interacting particle systems, gradient flow analysis, and control theory. This area of study is inherently tied to machine learning, given the prevalence of Transformers in numerous large language models. Through mathematical analysis, we aim to elucidate their inherent properties and, perhaps, enhance their performance.

Before this, during my Phd, I worked mostly on subelliptic operators, in relation with control theory, spectral theory, and propagation of waves. My two main PhD results are a proof of the impossibility of controlling or observing linear subelliptic wave equations, and the description of the propagation of subelliptic waves along abnormal geodesics.