Olivier Bisson Inria · Université Côte d’Azur · Nice, France
Portrait of Olivier Bisson

Olivier Bisson

PhD student in Geometric Statistics at Inria, Université Côte d’Azur

I work on geometric statistics with a focus on applied differential geometry to statistical manifolds. My current interests include Riemannian/quotient geometry on SPD and full-rank correlation matrices, log-Euclidean metrics for statistics on matrix manifolds, orbit-type stratification and geometry of rank-deficient limits.

Matrix manifolds Log-Euclidean geometry SPD matrices Correlation matrices Orbit-type stratification Riemannian submersion Principal bundles

Quick links: CV · Google Scholar

Contact

Email: olivier.bisson@inria.fr
Office: Fermat, room F202
Postal address: Inria, 2004 Rte des Lucioles, 06560 Valbonne

Research

My research develops differential-geometric tools for statistics on matrix manifolds, with a focus on symmetric positive-definite (SPD) matrices and full-rank correlation matrices. I study how geometric choices—especially log-Euclidean metrics and quotient constructions—shape geodesics, Fréchet means, polynomial regressions... and how these models behave near rank-deficient limits through orbit-type stratification. A recurring goal is to keep the geometry mathematically faithful while remaining computationally practical for real data, such as dynamic functional connectivity.

  • Riemannian and quotient geometry on SPD and correlation manifolds (principal-bundle, Riemannian submersion).
  • Log-Euclidean frameworks for efficient statistical computations (geodesics, means, trajectories).
  • Differential calculus for quotient-geodesic computations (e.g., derivative of the stretch tensor).
  • Extensions toward rank-deficient boundaries (stratified/PSD limits and finite-distance strata).
  • Open-source contributions: implementations of several Riemannian metrics and matrix manifolds in geomstats.

(Pre)Publications

Olivier Bisson, Xavier Pennec. Log-Euclidean Lie Groups. arXiv
arXiv preprint arXiv:2511.13380 (2025).
Olivier Bisson, Yanis Aeschlimann, Samuel Deslauriers-Gauthier, Xavier Pennec. Log-Euclidean Frameworks for Smooth Brain Connectivity Trajectories. arXiv DOI
International Conference on Geometric Science of Information (GSI 2025), pp. 194–204. Springer. DOI: 10.1007/978-3-032-03924-8_20. (Nominated for Best Paper Award.)
Olivier Bisson, Xavier Pennec. Differential of the Stretch Tensor for Any Dimension with Applications to Quotient Geodesics. PDF DOI
Comptes Rendus. Mathématique, 362 (2024), pp. 1847–1856. DOI: 10.5802/crmath.692.

Talks & Conferences

Mini-course: Quotient Spaces and Related Differential Geometry
EPIONE Seminar, Inria Sophia Antipolis, France — 12 Dec. 2025.
Log-Euclidean Frameworks for Smooth Brain Connectivity Trajectories
Geometric Science of Information (GSI), St Malo, France — 29 Oct. 2025. (nominated for Best Paper Award.)
Geometry, Stratification and Applications of Structured Correlation Matrices
EPIONE Seminar, Inria Sophia Antipolis, France — 5 Mar. 2025.
Differentiable Structures on Correlation Matrices and Applications in Neuroimaging
Infinite-dimensional Geometry: Theory and Applications, ESI (Vienna), Austria — 10 Feb. 2025.
Geometry, Stratification and Applications of Structured Correlation Matrices
3IA Côte d’Azur PhD Seminar, Nice, France — 6 Dec. 2024.
Riemannian Metrics on Correlation Matrices with Applications in Neuroimaging
Mathematical Imaging and Random Geometry (RT MAIAGES), Nice, France — 25 Nov. 2024.
Introduction to the Riemannian Geometry of Correlation Matrices
EPIONE Seminar, Inria Sophia Antipolis, France — 18 Oct. 2024.
A framework to put metrics on quotient spaces, with application in medical image analysis
EPIONE annual retreat, Auron, France — Feb. 2024.
Poster: Geometry, stratification and applications of structured correlation matrices
3IA scientific day, SKEMA, Sophia Antipolis, France — Dec. 2023.
A framework to put metrics on quotient spaces, with application in medical image analysis
EPIONE Seminar, Inria Sophia Antipolis, France — Oct. 2023.

Teaching

Introduction à l’analyse (L1) — Université Côte d’Azur
2025–2026 · Teaching assistant (TD). Topics: sets & functions, limits/continuity, differentiability, function study, injective/surjective/bijective maps, integrals & primitives.
Compléments d’algèbre linéaire (L2) — Université Côte d’Azur
2024–2025 · Teaching assistant (TD). Topics: orthogonality and projections, Gram–Schmidt, least squares, isometries, PCA (intro).
Calculus II (L2) — Université Côte d’Azur
2024–2025 · Teaching assistant (TD). Topics: complex numbers, linear ODEs, multivariable calculus (partials, gradient, tangent plane, level sets, local extrema).
Maths Approfondissement 2 (L1) — Université Côte d’Azur
2023–2024 · Teaching assistant (TD). Topics: exponential/logarithm refreshers, linear ODEs, Riemann integration basics, partial fraction decomposition, Euclidean vector geometry.

Personal

I come from south of France and I enjoy rock climbing, sailing, beach volleyball, going out and traveling. I love the sea. I am deeply conviced that anyone can do maths.

Live a life of ease