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Explore hidden symmetries in fluid dynamics through this fifth lecture of a minicourse presented by Professors Alexei Mailybaev and Simon Thalabard. Delve into the theoretical foundations of recently discovered projective symmetries in fluid dynamics equations, examining their algebraic structure for both deterministic and statistical formulations. Gain insights into how these symmetries underpin phenomena like Kolmogorov self-similarity and intermittency in hydrodynamic turbulence. Analyze examples ranging from rigorously solvable models to numerical challenges in fluid dynamics equations. Part of an eight-lecture series held at the Instituto de Matemática Pura e Aplicada (IMPA) in January 2024, this session offers a deep dive into advanced mathematical concepts at the intersection of symmetry and fluid mechanics.
