Explore the concept of free Stein dimension in this 47-minute lecture from the Hausdorff Center for Mathematics. Delve into the world of tracial von Neumann algebras and finitely generated *-subalgebras, understanding how free Stein dimension serves as a free probabilistic invariant. Learn about its computation for various examples and discover how its quantitative behavior can unveil structural properties of von Neuman algebras. Gain insights from the joint work of Brent Nelson and Ian Charlesworth as they introduce this fascinating mathematical concept and its applications.