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 study differential geometry and geometric statistics on smooth manifolds and stratified spaces, with a focus on correlation matrices across ranks. My work connects quotient geometry, orbit-type stratification, and rank-constrained geodesics, alongside log-Euclidean methods for matrix-valued data.

My PhD defense is scheduled for 12 November 2026, under the supervision of Xavier Pennec.

I am seeking postdoctoral opportunities in differential geometry and geometric statistics.

Stratified spaces Quotient geometry Correlation matrices Rank-constrained geodesics Curvature & holonomy Geometric statistics Log-Euclidean geometry

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 concerns the geometry of spaces with rank constraints and singularities, especially correlation matrices viewed as quotients of products of spheres. I study how the Riemannian geometry of each fixed-rank stratum relates to the intrinsic length geometry of the whole stratified space. Questions about geodesics, curvature, holonomy, and volume measures connect these structures to geometric statistics and applications in brain connectivity.

  • Stratified and quotient geometry: orbit-type stratifications, fixed-rank reduction, intrinsic distances, and rank-constrained geodesics.
  • Connections, curvature, and holonomy: mechanical connections and horizontal lifts in matrix quotient spaces.
  • Volume and probability: quotient Riemannian volume, Euclidean surface measures, and sampling on low-rank correlation spaces.
  • Log-Euclidean geometry: isometries and quotient metrics on positive-definite and full-rank correlation matrices.
  • Geometric statistics: Fréchet means, regression, and smooth brain connectivity trajectories; open-source contributions to geomstats.

Publications

Preprints

Olivier Bisson, David Loiseaux, Xavier Pennec. On the Geometry of Low Rank Correlation Matrices.
arXiv preprint, 2026.
arXiv:2610.28475
Olivier Bisson, Xavier Pennec. Log-Euclidean Lie Groups.
arXiv preprint, 2025.
arXiv:2511.13380

Journal papers

Olivier Bisson, Xavier Pennec. Differential of the Stretch Tensor for Any Dimension with Applications to Quotient Geodesics.
Comptes Rendus. Mathématique, 362 (2024), pp. 1847–1856.
DOIPDF

Conference papers

Olivier Bisson, Yanis Aeschlimann, Samuel Deslauriers-Gauthier, Xavier Pennec. Log-Euclidean Frameworks for Smooth Brain Connectivity Trajectories.
Geometric Science of Information (GSI 2025), pp. 194–204. Springer. Nominated for Best Paper Award.
DOIarXiv

Selected talks & conferences

A selection of presentations, including a conference poster. The CV contains the full list.

On the Geometry of Low Rank Correlation Matrices
Statistical Foundations for the Analysis of Non-Euclidean Data, Institute for Mathematical and Statistical Innovation (IMSI), University of Chicago, Chicago, USA — 21 Oct. 2026.
Poster: Log-Euclidean Lie Groups and rs-fMRI Brain Connectivity Trajectories
Foundations of Computational Mathematics (FoCM), Faculty of Mathematics, University of Vienna, Austria — 8–18 July 2026.
Log-Euclidean Geometry of Full-Rank Correlation Matrices
Geometry, Topology and Machine Learning 2026 (GML 2026), Sorbonne Université, Paris, France — 18–22 May 2026.
Log-Euclidean Frameworks for Smooth Brain Connectivity Trajectories
Geometric Science of Information (GSI), St Malo, France — 29 Oct. 2025. Nominated for Best Paper Award.
Differentiable Structures on Correlation Matrices and Applications in Neuroimaging
Infinite-dimensional Geometry: Theory and Applications, ESI (Vienna), Austria — 10 Feb. 2025.
Riemannian Metrics on Correlation Matrices with Applications in Neuroimaging
Mathematical Imaging and Random Geometry (RT MAIAGES), Nice, France — 25 Nov. 2024.

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