Über das β-Acetacetylpyridyl

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Affine Kac-Moody algebras and semi-infinite flag manifolds

We study representations of affine Kac-Moody algebras from a geometric point of view. It is shown that Wakimoto modules introduced in [18], which are important in conformal field theory, correspond to certain sheaves on a semi-infinite flag manifold with support on its Schhubert cells. This manifold is equipped with a remarkable semi-infinite structure, which is discussed; in particular, the semi-infinite homology of this manifold is computed. The Cousin-Grothendieck resolution of an invertible sheaf on a semi-infinite flag manifold gives a two-sided resolution of an irreducible representation of an affine algebras, consisting of Wakimoto modules. This is just the BRST complex. As a byproduct we compute the homology of an algebra of currents on the real line with values in a nilpotent Lie algebra.Dedicated to Dmitry Borisovich Fuchs on his 50th birthdayAddress after September 15, 1989: Mathematics Department, Harvard University, Cambrdige, MA 02138, USA     

Instabilities in thermal gravity with a cosmological constant

It is shown that in quantum gravity at finite temperature, the effective potential evaluated in the tadpole approximation can have a local minimum below a certain critical temperature. However, when the leading higher order thermal loop corrections are included, one finds that no static solution exists at high temperature.     

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Invited Lecture. Columnar ordering as an excluded-volume effect

The nature of the possible liquid-crystalline phases that a molecular or colloidal system may exhibit depends sensitively on the shape of the constituent particles. Recent computer simulations on fluids of consisting of non-spherical hard-core molecules suggest that, in order to predict the relative stability of isotropic, nematic, smectic and columnar phases in such very simple model fluids, it is not enough to characterize the molecular shape by an overall length-to-width ratio. New results of computer simulations on a model for disc-like molecules clearly illustrate this point.