Cardiff

Some of the most studied examples of conformal field theories
include
the Wess-Zumino-Witten models. These are conformal field theories exhibiting
affine Lie algebra symmetry at non-negative integers levels. In this talk I
will
discuss conformal field theories exhibiting affine Lie algebra symmetry at
certain rational (hence fractional) levels whose structure is arguably even
more intricate than the structure of the non-negative integer levels,
provided
one is prepared to look beyond highest weight modules.

It is an inherent premise in Boltzmann's formulation of linear viscoelasticity, that for shear deformations at constant pressure and constant temperature, every material has a unique continuous relaxation spectrum. This spectrum defines the memory kernel of the material. Only a few models for representing the continuous spectrum have been proposed, and these are entirely empirical in nature.

Extensive laboratory time is spent worldwide in collecting dynamic data from which the relaxation spectra of different materials may be inferred. In general the process involves the solution of one or more exponentially ill-posed inverse problems.

In this talk I shall present rigorous models for the continuous relaxation spectrum. These arise naturally from the theory of continuous wavelet transforms. In solving the inverse problem I shall discuss the role of sparsity as one means of regularization, but there is also a secondary regularization parameter which is linked, as always, to resolution. The topic of model-induced super-resolution is discussed, and I shall give numerical results for both synthetic and real experimental data.

The talk is based on joint work with Neil Goulding (Cardiff University).