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Explore the fascinating world of billiards in mathematics through this 34-minute lecture by Alejandro Kocsard from the Instituto de Matemática Pura e Aplicada. Dive into the mathematical principles behind billiard dynamics, examining how geometric shapes and trajectories influence the behavior of billiard balls. Learn about the connections between billiards and various areas of mathematics, including dynamical systems, geometry, and ergodic theory. Discover how this seemingly simple game can lead to complex mathematical problems and insights. Gain a deeper understanding of the research conducted under the Bolsa Cientista do Nosso Estado program, showcasing the importance of mathematical research in advancing scientific knowledge.