Résumé : Information geometry is an interdisciplinary field that uses the tools of differential geometry to explore and analyze probability theory and statistics. It focuses on statistical manifolds, geometric spaces (Riemannian manifolds) whose points represent different probability distributions. This geometric perspective provides powerful insights into many fields among which information theory. In this talk, I will present basic ideas about how to connect geometry and statistics, in particular statistical manifolds and their Fisher metric. Finally, closer to my current research themes, a statistical approach is discussed through the introduction of dual affine connections associated with the metric on almost Kähler manifolds. This research is motivated by the Goldberg conjecture, which asserts that a compact symplectic manifold $(M, \omega)$ endowed with an $\omega$-compatible Einstein metric is Kähler.

Dernière modification : Thursday 16 October 2025

Contact pour cette page : Cyril.Banderier at lipn.univ-paris13.fr