GTA Seminar | Speaker: Mirjana Milijevic,  University of Banja Luka, Bosnia and Herzegovina
 

Title: Geometry of Statistical Manifolds

Abstract: Statistical manifolds provide a natural geometric framework for studying statistical models and their underlying differential structures. Unlike Riemannian manifolds, which are equipped with a metric and its Levi-Civita connection, statistical manifolds admit a pair of torsion-free affine connections that are dual with respect to a Riemannian metric. This additional structure gives rise to a rich geometry with connections to information geometry, probability theory, and differential geometry.

In this talk, we introduce the fundamental concepts of statistical manifolds, emphasizing the role of dual connections, the difference tensor, and curvature. We then discuss selected geometric properties of statistical manifolds, focusing on the interplay between their Riemannian and affine structures. Particular attention will be given to geometric constructions involving compatible tensor fields and to the geometry of statistical submanifolds.

The aim is to illustrate how classical ideas from Riemannian geometry can be extended to the statistical setting, highlighting both the additional geometric flexibility and some questions that arise naturally in this broader framework.