Abstracts

Franz Merkl

A Riemann Roch Theorem for Infinite Genus Riemann Surfaces with Applications to Inverse Spectral Theory

Abstract: Riemann surfaces of infinite genus arise in a natural way as spectral varieties of several partial differential equations in mathematical physics. In the talk, a theorem of Riemann-Roch type is introduced which applies to the natural Bloch line bundle over the spectral curve of the heat equation with a space- and time-dependent periodic potential. The solution of the inverse spectral problem for this heat equation is an application of this theorem.

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Jörg Teschner

On Structure Constants, Spectrum and Fusion Rules in some noncompact Conformal Field Theories

Abstract: Methods to determine Structure Constants, Spectrum and Fusion Rules for noncompact Conformal Field Theories will be presented in the examples of Liouville theory and SL(2,C)/SU(2) WZNW model. They combine results from the bootstrap approach (Shifts on the set of "principal series" representations via fusion with degenerate reprs.) with canonical quantization. Some beautiful analogies to harmonic analysis on noncompact spaces are found which together with the results obtained so far should help to pave the way for a full mathematically rigorous treatment.

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Marcus Grote

Modeling Geophysical Flows Via Large Scale Statistical Theories

Abstract: An important practical issue for modeling fluid flows which exhibit organized large scale structures, such as geophysical flows in the ocean and the atmosphere, involves the development of crude closure models. Such crude closure dynamics should quantitatively capture evolving nonlinear large scale behavior with reasonable accuracy via the evolution of a small number of parameters. Here we propose and develop crude closure dynamics based on equilibrium large scale statistical theories involving only a few constraints. The crude closure algorithms are tested systematically through numerical experiments with the Navier-Stokes equations in two dimensions on simple geometries with strong small scale random forcing at moderately large Reynolds numbers. The results of numerical experiments, which include geophysical effects such as Ekman drag and underlying topography, will also be presented.

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Jürgen Fuchs

Automorphisms of Kac-Moody algebras and isomorphisms of chiral blocks

Abstract: We construct certain outer automorphisms of affine Kac-Moody algebras and implement them on integrable highest weight modules. To these automorphisms we associate isomorphisms between bundles of chiral blocks of WZW theories. These bundle-isomorphisms respect the Knizhnik-Zamolodchikov connection and have finite order. In the case where the bundle-isomorphism is an endomorphism, the bundle of chiral blocks is shown to be a reducible vector bundle. A conjecture for the trace of such endomorphisms is presented; it generalizes the Verlinde formula and is compatible with factorization.

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