Title: Quantum footprints of symplectic rigidity
Abstract: I'll discuss an interaction between symplectic topology, a rapidly developing mathematical area originated as a geometric language for problems of classical mechanics, and quantum mechanics. On one hand, ideas from quantum mechanics give rise to new structures on the symplectic side, and quantum mechanical insights lead to useful symplectic predictions. On the other hand, some phenomena discovered within symplectic topology admit a translation into the language of quantum mechanics.