3:00–4:00 pm
Big Fiber Theorems and Ideal-Valued Measures
Abstract: In various fields of mathematics one encounters statements of the following type: For any map in a suitable class there is a point in the target whose preimage is ``big". This includes the Centerpoint Theorem in combinatorial geometry, the Maximal Fiber Inequality in topology, and the Non-Displaceable Fiber Theorem in symplectic topology. I'll present a unified viewpoint at these results based on Gromov's notion of ideal-valued measures and its adaptation to symplectic topology. Joint work with Adi Dickstein, Yaniv Ganor, and Frol Zapolsky.
This talk will be followed by a short course over the next few weeks expanding on these ideas. (Details will be announced in a future email and on our web page; Leonid's lectures will be followed by a course by Danny Calegari on the foundations of symplectic topology).