Research topics

My research field is geometric analysis. I'm especially interested in certain classes of metric measure spaces obtained as Gromov-Hausdorff limits of Riemannian manifold.

Other keywords: Riemannian geometry, non-smooth geometry, geometric flows, PI spaces, Dirichlet forms, optimal transport, manifold learning.

Preprints:

• Critical metrics of eigenvalue functionals via Clarke subdifferential, with R. Petrides (Université Paris Cité), 2024.
• Kato meets Bakry-Émery, with G. Carron (Nantes Université) et I. Mondello (Université Paris-Est Créteil), 2023.
• Limits of manifolds with a Kato bound on the Ricci curvature. II, with G. Carron (Nantes Université) and I. Mondello (Université Paris-Est Créteil), 2022.

Publications:

• Symmetrized and non-symmetrized Asymptotic Mean Value Laplacian in metric measure spaces, with A. Mine (KTH Stockholm), 2022. To appear in Proceedings of the Royal Society of Edinburgh Section A: Mathematics.

• Limits of manifolds with a Kato bound on the Ricci curvature, with G. Carron (Nantes Université) and I. Mondello (Université Paris-Est Créteil).

  to appear soon at Geometry and Topology.

• Torus stability under Kato bounds on the Ricci curvature, with G. Carron (Nantes Université) and I. Mondello (Université Paris-Est Créteil).

  Journal of the London Mathematical Society,  Volume 107, Issue 3,  943--972, 2023.

• A rigidity result for metric measure spaces with Euclidean heat kernel, with G. Carron (Nantes Université).
  Journal de l’École Polytechnique — Mathématiques, Tome 9, 101-154, 2022.
• Adimensional weighted Sobolev inequalities in PI spaces.                                Annales Fennici Mathematici, 47(1), 351–379, 2022.
• Embedding of RCD*(K,N) spaces in L^2 via eigenfuntions, with L. Ambrosio (SNS Pise), S. Honda (Tohoku University) and J. Portegies (Eindhoven University).
• Journal of Functional Analysis, Volume 280, Issue 10, 108968, 2021.
• Weighted Sobolev Inequalities in CD(0,N) spaces.                                              ESAIM: Control, Optimisation and Calculus of Variations,  Volume 27,  Paper No. S22, 2021.
• Asymptotic Mean Value Laplacian in Metric Measure Spaces, with A. Minne (KTH Stockholm).                                                                                              Journal of Mathematical Analysis and Applications, Volume 491, Issue 2, 124330, 2020.

• Short-time behavior of the heat kernel and Weyl's law on RCD*(K, N) spaces, with L. Ambrosio (SNS Pise) and S. Honda (Tohoku University).                          Annals of Global Analysis and Geometry, Volume 53, Issue 1, 97-119, 2018.

Proceedings:

• A survey on spectral embeddings and their application in data analysis.        Actes du séminaire de Théorie Spectrale et Géométrie, Fourier Institute (Grenoble), Tome 35 (2017-2019) , 197-244.

• 2023. Conference "Geometric Analysis", Regensburg Universität, Allemagne.
• 2022. Conference "From Dirichlet Forms to Wasserstein Geometry", HCM, Bonn, Allemagne.
• 2022. Geometric structures research seminar, SISSA, Trieste, Italie.
• 2021. Summer school "Curvature Constraints and Spaces of Metrics", Institut Fourier, Grenoble, France.
• 2021. Research group on Topological Data Analysis, IMAG Montpellier, France.
• 2020. Geometric Day in Créteil, Université de Créteil, France.
• 2019. Geometry Seminar, Tohoku University, Sendai, Japon.

• 2019. Simons Semester Seminar, Mathematical Institute of the Polish Academy of Sciences, Varsovie, Pologne.

• 2019. Wokshop: ``Geometric Aspects of Harmonic Analysis and Spectral Theory'', Technion, Haifa, Israel.
• 2019. Séminaire Gaston Darboux, Institut Montpellierain Alexandre Grothendieck, Montpellier, France.

• 2019. Séminaire Théorie Spectrale et Géométrie, Institut Fourier, Grenoble, France.

• 2018. Séminaire de Géométrie, Université de Tours, France.

• 2018. Mini-Workshop: ``Nonsmooth Geometry and Optimal Transport'', Scuola Normale Superiore di Pisa, Pise, Italie.

• 2017. Séminaire de Géométrie, Université Paris-Diderot, Paris, France.