# Contractions of Lie groups: an application of Physics in Pure Mathematics

18 February 2014
17:00
to
18:15
Tony Dooley
Abstract
Contractions of Lie groups have been used by physicists to understand how classical physics is the limit as the speed of light tends to infinity" of relativistic physics. It turns out that a contraction can be understood as an approximate homomorphism between two Lie algebras or Lie groups, and we can use this to transfer harmonic analysis from a group to its limit", finding relationships which generalise the traditional results that the Fourier transform on $\R$ is the limit of Fourier series on $\TT$. We can transfer $L^p$ estimates, solutions of differential operators, etc. The interesting limiting relationship between the representation theory of the groups involved can be understood geometrically via the Kirillov orbit method.
• Functional Analysis Seminar