This is a joint meeting of the Geometric Analysis and PU/IAS Symplectic Geometry Seminar.

I will discuss the Poisson bracket invariant of a cover, which
was introduced by L. Polterovich. Initially, this invariant was studied via
Floer theory, and lower bounds for it were established in some situations.
I will explain how one can obtain the conjectural lower bound in dimension
2, using only elementary arguments. This is a joint work with A. Logunov and
S. Tanny. We express our gratitude to F. Nazarov for his contribution to
this work.