Title: Big fiber theorems, ideal-valued measures, and symplectic topology
Abstract: I will discuss an adaptation of Gromov's ideal-valued measures to symplectic topology. It leads to a unified viewpoint on three 'big fiber theorems': the Centerpoint Theorem in combinatorial geometry, the Maximal Fiber Inequality in topology, and the Non-displaceable Fiber Theorem in symplectic topology—and yields applications to symplectic rigidity.
Joint work with Adi Dickstein, Yaniv Ganor, and Frol Zapolsky.