Gromov's celebrated "Nonsqueezing Theorem" states that one cannot "squeeze" a symplectic ball into a thin cylinder using a symplectic transformation. This shows that symplectic diffeomorphisms are more rigid that volume preserving ones, and that there exists a notion of "size" peculiar to symplectic object. In this talk, I will explain the linear version of this theorem.

Everyone interested in symplectic geometry / topology is welcome.

Abstract: To start this year's NCG seminar series, I shall give a quick survey of one of the jewel's of functional analysis, namely Gelfand's theory of commutative Banach algebras. This will naturally lead to Gelfand-Naimark's characterization of commutative C*-algebras and the notion of noncommutative space. I shall give several key examples and applications illustrating the power of Gelfand's old theory going back to the years 1939-1943!