York Analysis Seminars, Autumn Term 1999
Final programme.
Talks are in Vanbrugh College, room V/131, at 11:15 every (well, almost
every!) Wednesday morning during term. Coffee beforehand in the common
room opposite (V/135) at 11:00. Everybody welcome!
- Wednesday 20th October 1999
- Speaker: Simon Eveson
- Title: Norms of iterates of Volterra operators (II)
- Abstract: Last term I gave a talk in which I reproduced earlier
results by Kershaw and Thorpe on the speed of decay of ||V^n||
where V is the indefinite integration operator acting on the
Hilbert space L^2[0,1]. In this talk I shall discuss
generalisations to a wide class of Volterra convolution operators.
- Wednesday 27th October 1999
- Speaker: Maurice Dodson
- Title: The theorems of Shannon and Plancherel: energy conservation in
communication theory
- Wednesday 3rd November 1999
- Speaker: Ian McIntosh
- Title: New Soap Bubbles
- Abstract: The geometric characterisation of a soap bubble is that
it is a surface of constant mean curvature. Another
characterisation is that its Gauss map is a harmonic map to the
2-sphere. All such maps arise from solving an ODE with values in a
loop group. The talk will aim to explain how this works and
present some new surfaces obtained by implementing this
procedure. The phrase "integrable system" will be mentioned, not
just in passing and not without some justification.
- Wednesday 10th November 1999
- Speaker: Birgit Jacob (Leeds)
- Title: On the continuity and boundedness of the spectral
factorization mapping
- Wednesday 24th November 1999
- Speaker: Vladimir Kisil (Leeds)
- Title: Non-Commutative Geometry: Algebra, Analysis, and Symmetries
- Abstract: It was realized during last 50 years that many structures
of functional analysis could be viewed as non-commutative counterparts
of fundamental geometric objects. For example, a positive linear
functional on a noncommutative Banach algebra correspond to an
additive measure on a set. Such an approach explores interesting
connections between algebra, geometry, and analysis. The transition
from commutative to non-commutative spaces is often associated with
quantization. We give an elementary overview of this topic.
- Wednesday 1st December 1999
- Speaker: Chris Wood
- Title: Global Analysis on the 3-Sphere
- Abstract: I will be discussing the energy of unit vector fields on
the 3-dimensional sphere (that is, the unit sphere in 4-space).
Since the talk involves an element of surprise, I shall not
provide any further details here!
- Wednesday 8th December 1999
- Speaker: Jonathan Partington (Leeds)
- Title: Approximation in Hilbert spaces of analytic functions
- Abstract: Several problems involving approximation in Hilbert
spaces of analytic functions, including Hardy spaces and
Paley-Wiener spaces, can be put into a general framework and
solved using operator theory. We shall touch lightly on some
of the applications, which include Systems Identification,
Signal Processing and Inverse Problems for PDEs.
- Wednesday 15th December 1999
- Speaker: Chris Fewster
- Title: Microlocal analysis and quantum inequalities
- Abstract: Microlocal analysis provides powerful tools for analysing
the singularities of distributions. I will give a short introduction
to some aspects of microlocal analysis, and then describe a recent
application of these techniques to derive rigorous and general
`quantum inequalities'. These results provide lower bounds on the
averaged energy density of a quantum field measured by an observer.
Please contact Simon Eveson for any
further information.
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