Summary
I am currently a PhD. student at the Mathematics Department of the Université Libre de Bruxelles, under the supervision of Bruno Premoselli.
My research is supported by a FRS-FNRS FRIA grant.
Research interests
- Elliptic partial differential equations on manifolds
- Nonlinear and geometric analysis
- Critical nonlinear polyharmonic equations
Education
- Bachelor and master degree at Université libre de Bruxelles
Research
My main research interest is the understanding of the structural properties of the set of solutions to critical nonlinear polyharmonic equations on compact Riemannian manifolds. I study the properties of sequences of solutions to equations involving a linear elliptic operator whose leading-order term is an integer power of the Laplacian, and where the non-linearity comes from the corresponding critical Sobolev exponent. These solutions commonly exhibit a blowing-up behavior, which needs to be understood by means of asymptotic analysis techniques.
Such equations arise naturally in various geometrical contexts, such as studying the optimal constants in the critical Sobolev embedding on closed manifolds, or when trying to prescribe higher-order analogs of the scalar curvature in the conformal class of the manifold's metric.
Publications and preprints
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Attaining the optimal constant for higher-order Sobolev inequalities on manifolds via asymptotic analysis,
Journal of the London Math. Soc., Vol. 111, e70170, 2025 (preprint available on ArXiv).
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The Green's function of polyharmonic operators with diverging coefficients: Construction and sharp asymptotics,
Journal of Differential Equations, Vol. 419, 370-417, 2025 (preprint available on ArXiv).
Talks and posters
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SPP@ULB seminar (ULB, Bruxelles Belgium), Some blow-up phenomena in critical elliptic PDEs (slides), November 2024
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Nonlinear and Geometric Analysis in Nancy (IECL, Nancy France), The optimal constant for the critical Sobolev inequality of higher order on manifolds (slides), November 2024
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BMS PhD day (UAntwerp, Antwerp Belgium), The optimal constant for critical Sobolev embeddings on manifolds (slides), May 2024
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Young Researchers in PDEs (ICMAT, Madrid Spain), Asymptotic analysis of non-linear critical polyharmonic equations, sharp Sobolev embeddings on manifolds (poster), September 2023
Manuscripts
Teaching at ULB
Exercice classes
| 2023-2025 | Introduction aux équations aux dérivées partielles, 3rd year bachelor students |
| 2022-2025 | Calcul Differentiel et Intégral 2, 2nd year bachelor students |
Other
| 2023-2025 | Participation to Math.en.Jeans as researcher, aimed at popularizing mathematics to high-school students |
| 2022 | Student teaching assistant, Algèbre Linéaire et Géométrie, 1st year bachelor students |
