Watch a mathematics lecture exploring dimension theory and Lyapunov exponents, delivered by Mark Pollicott from the University of Warwick as part of the Simons Semester on Dynamics. Delve into the analysis of limit sets for conformal iterated function schemes with open set conditions, examining various methodologies for calculating Hausdorff and Box counting dimensions. Explore practical applications in number theory through Lagrange spectra, understand the behavior of Lyapunov exponents in random matrix products, and discover their connection to barycentric divisions of triangles. The 37-minute presentation covers fundamental concepts including Julia sets, fixing groups, and dimensional analysis through carefully constructed examples.