I'm mainly interseted in:
Geometry and Topology of Singularities.
Sobolev spaces on singular domains.
Geometric modeling.
Computer vision.
Machine learning.
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. (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.
Regularized LSTM models for cleaning multivariate time series from low-cost sensors for pollen detection in the air, with Pierre Houedry, Valérie Monbet, Johann Lauthier & Houssam El Azari, Stochastic Environmental Research and Risk Assessment, Volume 40, article number 173 (2026).
Abstract: Low-cost environmental sensors are increasingly used for real-time monitoring, but they often suffer from limitations such as accuracy, calibration drift, short lifespan, and sensitivity to environmental factors. These issues are particularly evident in airborne pollen monitoring devices like Beenose, which provide live high-frequency data yet frequently deviate from manual reference methods such as Hirst traps. To address some of these challenges, we propose a deep learning framework for anomaly correction in multivariate time series collected from Beenose sensors, using Hirst trap measurements as a free anomaly reference. Our approach extends LSTM-based autoencoders with a penalized loss function that explicitly integrates the reference data. The main contributions are: (i) the introduction of data augmentation strategies to address limited training data, and (ii) the adaptation of an LSTM-based autoencoder trained with a regularized loss function. Ablation experiments show that the main performance gain comes from the reference-based regularization term, while the architectural components play a complementary role