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A seminar talk from the Symplectic Geometry series where Jun Zhang from the University of Science and Technology China presents a proof of the quantitative contact big fiber theorem. Explore how this proof utilizes invariants derived from contact Hamiltonian Floer homology to demonstrate that any contact involutive map on a Liouville fillable contact manifold must have at least one non-displaceable fiber, provided the Liouville filling has non-vanishing symplectic homology. Learn about the parallel proof recently developed by Sun-Uljarevic-Varolgunes using symplectic homology with compact support. Discover the proposed definition of partial contact quasi-state and contact quasi-measure, which serves as a contact analog to Entov-Polterovich's quasi-state machinery in symplectic settings. The presentation covers joint work with Igor Uljarevic and is scheduled for April 1, 2025, at Simonyi 101 with remote access available.
