Hidden symmetries in fluid dynamics

In this series of lectures we discuss the recently discovered hidden (projective) symmetries in equations of fluid dynamics. This includes their theoretical foundations related to the algebraic structure of symmetry groups for both deterministic and statistical formulations. Then we consider their applications to the theory of hydrodynamic turbulence by showing how these symmetries underline the phenomena of Kolmogorov self-similarity and intermittency. We discuss several examples from rigorously solvable models to numerical challenges in fluid dynamics equations. We plan 6 lectures during 3 weeks in January 2024.