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Explore the intricacies of hydrodynamics as an effective field theory in this comprehensive lecture delivered by Jay Armas at the Erwin Schrödinger International Institute for Mathematics and Physics. Delve into the crucial role of symmetries and patterns of symmetry breaking in constructing Euclidean thermal partition functions. Discover how this construction can be used to diagnose the types of symmetries broken in the ground state of exotic field theories, including higher-form, fractonic, and Carrollian field theories. Gain valuable insights into the progression from relativistic to Carroll hydrodynamics as part of the Thematic Programme on "Carrollian Physics and Holography" held at ESI in April 2024.
