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Explore advanced concepts in locally conformally symplectic (LCS) geometry through this mathematical lecture from the IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Zoominar. Delve into the theory of LCS manifolds, which generalize symplectic manifolds where the 2-form satisfies dω = η ∧ ω for a closed 1-form η rather than being closed. Discover how these manifolds behave like symplectic manifolds when η is exact, but resemble contact manifolds when η has no zeroes. Learn about the application of generating functions theory for Lagrangians in twisted cotangent bundles to define spectral selectors for Hamiltonian LCS diffeomorphisms of S^1 X R^2n X S^1 and S^1 X R^(2n+1). Examine the construction of LCS capacity for domains in S^1 X R^2n X S^1, leading to a version of the non-squeezing theorem on this manifold. Investigate the definition of partial orders on groups of compactly supported LCS Hamiltonian diffeomorphisms and bi-invariant metrics on these groups. Gain insights into cutting-edge research in symplectic geometry through work conducted in collaboration with Mélanie Bertelson and Margherita Sandon, presented by Pranav Chakravarthy from Université libre de Bruxelles.
