Adrien Guillaume Currier, speaking in the Institute for Advanced Study's Special Year Research Seminar, tackles locally conformally symplectic (LCS) manifolds, spaces that are symplectic only up to a locally defined positive scaling factor. He shows how familiar symplectic tools carry over to this setting, including an LCS version of the Weinstein neighborhood theorem and Moser's trick, but notes that rigidity results like the Arnold conjecture have resisted generalization. The core of the talk is his approach to closing that gap: using Morse theory together with derived sheaves to prove an LCS analogue of the Arnold conjecture on cotangent bundles. Delivered at Simonyi Hall to a research audience, the talk assumes familiarity with symplectic geometry and moves quickly through technical constructions, aimed at specialists working at the intersection of symplectic topology and sheaf-theoretic methods.