Title of the course: Introduction to Differential Geometry with Applications to Statistical Manifolds
Instructor: Assoc. Prof. Mirjana Milijević
Institution: University of Banja Luka, Faculty of Economics, Bosnia and Herzegovina
Dates: September 14–18, 2026
Prerequisites: Basic linear algebra and multivariable calculus. No prior knowledge of differential geometry is required.
Level: Advanced undergraduate / graduate
Abstract: This course provides an introduction to the basic concepts of differential geometry, with an emphasis on geometric structures that arise naturally in applications. We will discuss smooth manifolds, tangent spaces, vector fields, differential forms, Riemannian metrics, connections, and curvature. In the second part of the course, we will introduce the basic ideas of statistical manifolds and discuss how differential-geometric structures can be used to describe statistical models. The course is intended to provide both a self-contained introduction to differential geometry and a first glimpse into the interaction between geometry and statistics.
Language: English