Geometry and Quantum Mechanics

We all know Quantum Mechanics works. Almost everything in our everyday life is based on principles of
Quantum Mechanics one way or another: from cellular phones to stability of atoms and, therefore, to the
very existence of our Universe. Yet, every time the word "Quantum" is mentioned, it brings mystery and
uncertainty. Ever since the discovery of Quantum Mechanics 100 years ago, it baffled the greatest minds
of the 20th century. In this talk, I will review our quest for elusive mathematical framework that is supposed
to describe "quantization" which, at various stages of its development, infiltrated many areas of pure
mathematics, including geometry and representation theory. Could it be that, at last, we are close to t
he solution thanks to the powerful tools of the Fukaya category, Langlands duality, and mirror symmetry?