Explore the intricate world of wind-tree billiards and Lyapunov exponents of the Hodge in this 50-minute lecture by Anton Zorich. Delve into the mathematical concepts behind diffusion processes in billiard systems and their relationship to Lyapunov exponents. Gain insights into the complex dynamics of particle motion in periodic obstacle arrays and understand how these systems relate to the broader field of dynamical systems theory. Examine the connections between wind-tree billiards and Hodge theory, uncovering the underlying mathematical structures that govern these fascinating phenomena.