Exploring Information Geometry

Noémie Combe is a mathematician and research professor at the Léonard de Vinci University Pole. She has secured several prestigious research grants, serving as principal investigator and group leader of the renowned Polonez Bis 3 programme—funded by Horizon 2020—at the University of Warsaw. Prior to this, she led a Minerva Group at the Max Planck Society for five years, where her research received significant recognition and sustained support. She earned her degrees from the University of Geneva, and completed her PhD at the University of Aix—Marseille and Sorbonne University (Paris 6).Philippe Combe is an emeritus professor of Mathematical Physics at the University of Aix-Marseille, as well as a long‐standing member of the Centre for Theoretical Physics (CPT). Over a distinguished career spanning more than four decades, he has made foundational contributions to functional analysis, group theory, operator theory, geometry, statistics, and stochastic process. His work is characterized by high‐impact collaborations across Europe and beyond. In addition to his research, Philippe Combe has provided key leadership in the scientific community.Hanna Nencka is a distinguished invited researcher in the Polonez Bis 3-sponsored Research Group at the University of Warsaw. She has held tenured professorships at Columbia University (USA), the Polish Academy of Science, and the University of Madeira (Portugal). Her prolific scholarship includes over one hundred peer-reviewed publications in leading journals. Her pioneering contributions to mathematical physics have earned her international recognition and multiple research awards, namely from the Polish Academy of Sciences for outstanding work.

• Introduction.- Foundations of General Topology.- Topological and Modeled Manifolds.- Differentiability and Gateaux Derivatives.- Fiber Bundles.- Connections, Parallel Transport, and Sheafs.- Probability Theory, Measure Theory, and Statistics.- Categorical Structures in Probability and Measure Theory.- Categorical and Geometric Structures in Statistical Manifold Theory.- Frobenius Manifolds.- Unveiling the Hidden Geometry of Statistical Manifolds.- Statistical Frobenius Manifolds and Learning.