Research

I study the geometrical and topological properties of random submanifolds. These random objects are defined as the vanishing loci of Gaussian fields on an ambient Riemannian manifold. Their study is motivated by questions in real algebraic geometry and in semi-classical analysis. I am interested in random variables associated with these submanifolds, such as their volume, their Euler characteristics or their Betti numbers.

When our random submanifold has almost surely dimension 0, we get a random point process. In this case, I am interested in the short range attraction-repulsion between points of this process, as well as the clustering properties coming from the lack of long range correlations.

All my papers are available on the arXiv and on the open archive HAL.

1. M. Ancona and T. Letendre, Multijet bundles and application to the finiteness of moments for zeros of Gaussian fields, submitted. Preprint : arxiv:2307.10659.
2. M. Ancona and T. Letendre, Zeros of smooth stationary Gaussian processes, Electron. J. Probab., 26 (2021), 1-81. Preprint: arxiv:2007.03240.
3. M. Ancona and T. Letendre, Roots of Kostlan polynomials: moments, Law of Large Numbers and Central Limit Theorem, Ann. H. Lebesgue, 4 (2021), 1659-1703. Preprint: arXiv:1911.12182.
4. T. Letendre and H. Ueberschär, Random moments for the new eigenfunctions of point scatterers on rectangular flat tori, Ann. Henri Poincaré, 22 (2021), no. 6, 1783-1836. Preprint: arXiv:1910.04001.
5. T. Letendre and M. Puchol, Variance of the volume of random real algebraic submanifolds II, Indiana Univ. Math. J., 68 (2019), no. 6, 1649-1720. Preprint : arxiv:1707.09771.
6. T. Letendre, Variance of the volume of random real algebraic submanifolds, Trans. Amer. Math. Soc., 371 (2019), no. 6, 4129–4192. Preprint : arxiv:1608.05658.
7. T. Letendre, Expected volume and Euler characteristic of random submanifolds, J. Funct. Anal., 270 (2016), no. 8, 3047-3110. Preprint : arxiv:1408.2107.

Contributions to the study of random submanifolds, advisor : Damien Gayet.

My dissertation contains my first two papers (numbered 1 and 2 in the above list) plus an introductory chapter (in french).

2023

• Geometry and Topology, Paris.
• Conference on Random Nodal Domains, Rennes (beamer).

2022

• Probability and Statistics, Nice (beamer).
• Workshop Quantum Chaos, Randomness and Spectral Problems in Mathematical Physics, Paris (beamer).
• Topology and Dynamics seminar, Orsay (beamer).

2021

• Workshop on Point Processes and Applications, Lille (beamer).

2020

• Probability seminar, Rennes (beamer).
• Annual meeting of the Harmonic Analysis team, Orsay (beamer).
• Friday's probabilities, Paris (beamer).

2019

• Spectral Theory and Geometry seminar, Grenoble (beamer).
• Geometry seminar, Nantes (beamer).
• Stochastic Model workshop, Paris (beamer).
• Workshop on Random Real Algebraic Geometry, Güzelyurt (beamer).
• Conference on Random Nodal Sets, Rennes (beamer).

2018

• Harmonic Analysis seminar, Orsay (beamer).
• Functional Analysis seminar, Paris (beamer).
• Journées nancéiennes de Géométrie, Nancy (beamer).

2017

• Geometry seminar, Chambéry (beamer).
• Workshop on Random Polynomials, Montevideo (beamer).
• Geometry and Dynamics seminar, Lyon (beamer).
• Probability workshop, Paris (beamer).
• Darboux seminar, Montpellier (beamer).
• DynQua seminar, Paris (beamer).

2016

• Annual meeting of the Algebra, Geometry and Logic team, Lyon (beamer).
• Geometry, Topology and Dynamics seminar, Orsay (beamer).
• Geometries seminar, Lyon (beamer).
• Probability seminar, Rennes (beamer).
• Statistical Field Theory seminar, Lausanne (beamer).
• Complex Analysis and Geometry seminar, Paris (beamer).

2015

• Geometry and Dynamics seminar, Lyon.
• Ph.D students seminar, Lyon (beamer).
• Mathematical Physics seminar, Lille (beamer).