Certainty about uncertainty
Abstract: Heisenberg's Uncertainty Principle is the affirmation that one cannot know exactly the position and the momentum of a quantum particle.
This physical principle may be modelled mathematically by saying that a function and its Fourier transform cannot both be localised.
It will be examined two ways in which this mathematical statement may be made precise, one due to Weyl, in which uncertainty is measured as a variance of a probability distribution, and another due to Hardy, in which it is shown that Gaussians have important extremal properties.
Then it will be shown that this principle is manifested in other areas of analysis. For example, eigenfunctions of Laplacians on manifolds have very precisely specified spectral properties, and hence cannot be localised on the manifold, and kernel operators cannot be localised close to the diagonal if their spectra are also localised.
16 May 2.00 - 5.00 pm
17 May 2.00 - 5.00 pm
18 May 2.00 - 5.00 pm
21 May 2.00 - 5.00 pm
22 May 9.00 - 12.00 am