Abstract: Functions can exhibit structures much smaller that their finest Fourier components, in ways that are not only mathematically interesting but have implications in several areas of science, ranging from optics and quantum physics to signal processing. The lectures will include some or all of the following topics: Basics, shifted fourier transforms, phase–space interpretations (Wigner and Husimi functions), optical singularities (‘vorticulture’), supershifts in weak measurements, superoscillation statistics (in optical fields, backflow, Klein-Gordon and Dirac equations), quantum supershifts, sensitivity to noise, Goos-Hänchen and related shifts, proagation of superoscillations, radar superdirectivity and optical superresolution.

Biosketch: After graduating from Exeter and St Andrews, Michael Berry entered Bristol University, where he has been for more than twice as long he has not. He is a physicist, focusing on the physics of the mathematics…of the physics. Applications include the geometry of singularities (caustics on large scales, vortices on fine scales) in optics and other waves, connections between classical and quantum physics, and the physical asymptotics of divergent series. He delights in finding the arcane in the mundane – abstract and subtle concepts in familiar or dramatic phenomena: Singularities of smooth gradient maps in rainbows and tsunamis; The Laplace operator in oriental magic mirrors; Elliptic integrals in the polarization pattern of the clear blue sky; Geometry of twists and turns in quantum indistinguishability; Matrix degeneracies in overhead-projector transparencies; Gauss sums in the light beyond a humble diffraction grating. The lectures take place at 16.30 hrs each day. The Salam Distinguished Lecture Series is sponsored by the Kuwait Foundation for the Advancement of Science.