Watch a 48-minute conference talk exploring semi-arithmetic Fuchsian groups and finiteness results, delivered by Gregory Cosac from USP as part of a broader conference on hyperbolic geometry and group theory at IMPA. Learn about recent developments in hyperbolic geometry, focusing on the intersection of arithmetic and geometric group theory through the lens of Fuchsian groups. The talk was presented during a week-long conference organized in partnership with the Clay Mathematics Institute and NSF, featuring international speakers covering topics from hyperbolic manifolds to group actions and complex Morse theory. The conference was followed by a workshop aimed at graduate students, providing in-depth exploration of key topics through minicourses on exotic negatively curved manifolds, Coxeter polytopes, and arithmetic hyperbolic manifolds.