With the notion of interaction with oracles as a unifying theme of much of my dissertation work, I discuss novel models and results for property testing and computational learning, with the use of Fourier analytic and probabilistic methods.
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.