
Non-squeezing and Other Rigidity Results in LCS Geometry
Pranav Chakravarthy, a mathematician at the Université libre de Bruxelles, presents a research seminar talk given as part of the IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Zoominar. He addresses locally conformally symplectic (LCS) manifolds, a generalization of symplectic manifolds where the 2-form satisfies dω = η ∧ ω for a closed 1-form η, making them behave like symplectic manifolds when η is exact and like contact manifolds when η has no zeroes. Using generating functions for Lagrangians in the twisted cotangent bundle, Chakravarthy constructs spectral selectors for Hamiltonian LCS diffeomorphisms on S^1 x R^2n x S^1 and S^1 x R^(2n+1), building an LCS capacity that yields a version of the non-squeezing theorem on these spaces. Time permitting, he also sketches a partial order and a bi-invariant metric on the relevant diffeomorphism groups. The work is joint with Mélanie Bertelson and Margherita Sandon, and the talk assumes graduate-level familiarity with symplectic and contact geometry.