Seminar: Integrable Systems in Information Geometry: Geodesic Flows on Statistical Manifolds

We are pleased to announce an upcoming talk by Dr. Guilherme Feitosa de Almeida from the Max Planck Institute of Molecular Cell Biology and Genetics (MPI-CBG), who will be presenting on July 9, 2025, at 12:15.

Abstract:

Information geometry offers a powerful geometric framework to analyze statistical models, connecting probability theory with differential geometry. In this talk, I will explore the intersection of information geometry and differential equations by showing how geodesic equations on certain statistical manifolds, particularly those arising from exponential families, form integrable systems which is a class of solvable dynamical systems.

We begin with an overview of the geometric language essential to this theory: differentiable manifolds, Riemannian metrics (with a focus on the Fisher information metric), and geodesics.

The core of the presentation focuses on the statistical manifold of multivariate normal distributions, where we demonstrate that the associated geodesic equations constitute a completely integrable system. This integrability not only provides explicit analytical solutions but also facilitates efficient numerical computation of geodesics.

Throughout the talk, I will emphasize the rich mathematical structure of these systems and highlight how tools from integrable systems theory illuminate the behavior of information-geometric flows.