Pure Mathematics Seminar: Anthony Dooley
Anthony Dooley, University of Bath
Wednesday 24 April 2013, 1545-1645
A54, Postgraduate Statistics Centre Lecture Theatre
Please note early start time of 3.45pm.
Contractions of Lie groups: an application of Physics in Pure Mathematics
In order to explain the classical limit of relativistic physics, as the speed of light tends to infinity, physicists introduced the notion of a contraction of Lie algebras, where the structure constants of one algebra continuously deform to those of a (non-isomorphic) limit. Thus the Euclidean motion group of the plane is a contraction of the rotation group in three dimensions.
I shall describe an on-going research program where we have used contractions to study harmonic analysis on non-commutative Lie groups. One can obtain the representation theory, Fourier transforms, and solutions of differentiable operators on a contracted group from those of the contracting group.
This has allowed solution of some outstanding conjectures, eg the Herz asymmetry conjecture.