Welcome
I currently an Assistant professor (maître de conférence) in the Harmonic Analysis group of the Laboratoire de Mathématiques d'Orsay at the Université Paris-Saclay.
Research fields
My research interests lie in partial differential equations (PDEs), harmonic analysis, and geometric measure theory.
During my Ph.D., I focused on the $I$L^p$I$ boundedness of quadratic functionals and Riesz transforms in non-Euclidean spaces, such as graphs and Riemannian manifolds.
One of my key results demonstrated the $I$L^p$I$ boundedness ($I$ 1 < p \leq 2$I$) of the Riesz transform on fractal-like graphs, including those constructed from the Sierpinski gasket.
Currently, I am investigating boundary value problems on domains that are the complements of thin boundaries.
Together with Svitlana Mayboroda and Guy David, I have developed an elliptic theory for these domains using degenerate elliptic operators in divergence form.
Our research in this area explores the relationship between the geometry of the boundary and the regularity of solutions, in particular, we are looking for characterizations of uniformly rectifiable sets in terms of estimates on the harmonic measure and the Green function.