School of Mathematics

Mirror symmetry is a deep conjectural relationship between complex and symplectic geometry. It was first noticed by string theorists. Mathematicians became interested in it when string theorists used it to predict counts of curves on the quintic three-fold (just as there are famously 27 lines on a cubic surface, there are 2875 lines on a quintic three-fold, 609250 conics, and so on). Kontsevich conjectured that mirror symmetry should reflect a deeper equivalence of categories: his celebrated 'Homological Mirror Symmetry' conjecture.

We will present joint work with Will Merry. Using spectral invariants in Rabinowitz Floer homology we present an abstract contact non-squeezing theorem for periodic contact manifolds. We then exemplify this in concrete examples. Finally we explain connections to the existence of a biinvariant metric on contactomorphism groups. All this is connected and generalizes work by Eliashberg-Polterovich and Sandon.