Explore the fascinating world of higher genus surface flows in this 47-minute lecture by Corinna Ulcigrai. Delve into the intricate relationship between dynamics and 'arithmetics' as you learn about discrete dynamical systems, genus I surfaces, and arithmetic conditions. Discover the concepts of acceleration, mixing, and shearing, while gaining insights into local linearization and ergodic integrals. Engage with thought-provoking questions and explore future directions in this captivating mathematical journey presented by the International Mathematical Union.