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This lecture from the Colloque des sciences mathématiques du Québec (CSMQ) features Leonid Polterovich from Tel Aviv University and University of Chicago discussing the adaptation of Gromov's ideal-valued measures to symplectic topology. Explore how this approach provides a unified perspective on three significant 'big fiber theorems': the Centerpoint Theorem in combinatorial geometry, the Maximal Fiber Inequality in topology, and the Non-displaceable Fiber Theorem in symplectic topology. Discover the applications of these concepts to symplectic rigidity, based on joint work with Adi Dickstein, Yaniv Ganor, and Frol Zapolsky. The presentation was delivered on February 28, 2025, as part of the Centre de recherches mathématiques (CRM) activities.
