Mathematics Colloquium 2013 - 2014
All seminars are held in Room E/0.15, Senghennydd Road, Cardiff at 15:10 unless stated otherwise.
13th November 2013
Speaker: Professor Sir Michael Berry FRS (H H Wills Physics Laboratory, University of Bristol, UK)
Title: The singularities of light: intensity, phase, polarization.
Abstract: Geometry dominates modern optics, in which we understand light through its singularities. These are different at different levels of description. At the coarsest level, where light is described in terms of geometrical-optics rays, are the singularities of bright light: caustics - focal lines and surfaces (the envelopes of ray families), classified by the mathematics of catastrophe theory. Wave optics smooths these singularities and decorates them with rich interference patterns, widely applicable, for example to rainbows, ship wakes and quantum scattering. Wave optics introduces a new quantity, namely phase, which has its own singularities. These are optical vortices: geometrically, the singularities of dark light - lines in space, or points in the plane. They occur in all types of quantum or classical waves. On a finer scale, where the vector nature of light cannot be ignored, the new phenomenon is polarization. This possesses its own singularities, also geometrical. As well as representing physics at each level with associated mathematics, these optical and wave geometries illustrate the idea of asymptotically emergent phenomena.
4th December 2013
Speaker: Professor John King (University of Nottingham)
Title: Asymptotic behaviour in nonlinear diffusion.
Abstract: A variety of types of self-similarity can arise in classifying the asymptotic behaviour of parabolic partial differential equations, for example. A number of initial-value problems for a model nonlinear diffusion equation will be discussed, characterising in particular critical exponents and dimensions at which transitions occur.