Bounding the Poisson bracket invariant on surfaces

This lecture covers the concept of bounding the Poisson bracket invariant on surfaces, exploring joint work with A. Logunov and S. Tanny. It delves into the Poisson bracket, its cost and rigidity, and provides examples of non-displaceable surfaces. The lecture also discusses the functional (f, g) → || {f, g} || and the Cardin-Viterbo Theorem. Various topics such as displacement energy, Hofer's metric, and partition of unity are addressed, along with the quantitative version of bounding the Poisson bracket invariant. The lecture concludes with a detailed analysis of Poisson bracket rigidity and its implications.