Research interests

I'm mainly interseted in: 

• Geometry of Singularities.

• Subanalytic  geometry.

• Sobolev spaces on singular domains.

You can find here my papers and preprints:

• Regular projections and regular covers in o-minimal structures. Ann. Polon. Math.130.1(2023), 63-84. (you can find here the Arxiv  pdf). 

    Abstract: In this paper we prove that for any definable subset $X\subset \mathbb{R}^{n}$ in a polynomially bounded o- minimal structure, with $dim(X)<n$, there is a finite set of regular projections (in the sense of Mostowski ). We give also a weak version of this theorem in any o-minimal structure, and we give a counter example in o-minimal structures that are not polynomially bounded. As an application we show that in any o-minimal structure there exist a regular cover in the sense of Parusinski.

• Sobolev sheaves on the plane . Submitted to Annales de L'institut Fourier. (you can find here the Arxiv  pdf). 

    Abstract: In this paper, we show that for any integer $k \in \mathbb{N}$ there exists a Sobolev sheaf (in the sense of Lebeau ) on any definable site of $\mathbb{R}^2$ that agrees with Sobolev spaces on cuspidal domains. We also provide a complete computation of the cohomology of these sheaves using the notion of 'Good direction' introduced by Valette . This paper serves as an introduction to a more general project on the sheafification of Sobolev spaces in higher dimensions.