Welcome on the personal webpage

of David Tewodrose

My research is focused on the study of metric measure spaces. I'm interested in the tools that permit to make analysis on such spaces, with a particular taste for the heat kernel. Geometric aspects of certain classes of such spaces, like Gromov-Hausdorff limits of Riemannian manifolds, are also of my interest. In my thesis I worked on CD(0,N) and RCD(K,N) spaces, especially on spectral properties of compact RCD(K,N) spaces.

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

Preprints:

• Limits of manifolds with a Kato bound on the Ricci curvature, with G. Carron (Université de Nantes) et I. Mondello (Université de Créteil), 2021.
• A rigidity result for metric measure spaces with Euclidean heat kernel, with G. Carron (Université de Nantes), 2019.

Publications:

• Adimensional weighted Sobolev inequalities in PI spaces.                                                                                                                                                                        To appear in Annales Academiæ Scientiarum Fennicæ Mathematica, 2021.
• 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.

• 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.