the phase diagram of two-color QCD with the functional renormalization group. Universal aspects of deconfinement are illustrated mainly in the 2 + 1 dimensional SU(N) gauge theories with second order transition where many exact results from spin models can be exploited.

ACKNOWLEDGMENTS I would like to give many thanks to Dr. Shengli Fu and Dr. Yan Huang as my advi-

Abstract. We give a new proof of regularity of biharmonic maps from four-dimensional domains into spheres, showing first that the biharmonic map system is equivalent to a set of bilinear identities in divergence form. The method of reverse Hölder inequalities is used next to prove continuity

Abstract not found

We study Ginzburg–Landau equations for a complex vector order parameter Ψ = (ψ+, ψ−) ∈ C2. We consider the Dirichlet problem in the disk in R2 with a symmetric, degree-one boundary condition, and study its stability, in the sense of the spectrum of the second variation of the energy. We find

Abstract not found

de nationalité suisse et originaire de Zurich (ZH) et Lucerne (LU) acceptée sur proposition du jury:

Abstract not found

Abstract not found

mcmxciv This thesis deals with combinatorics in connection with Coxeter groups, finitely generated but not necessarily finite. The representation theory of groups as nonsingular matrices over a field is of immense theoretical importance, but also basic for computational group theory, where the group elements are data structures in a computer. Matrices are unnecessarily large structures, and part of this thesis is concerned with small and efficient representations of a large class of Coxeter groups (including most Coxeter groups that anyone ever payed any attention to.) The main contents of the thesis can be summarized as follows. • We prove that for all Coxeter graphs constructed from an n-path of unlabelled edges by adding a new labelled edge and a new vertex (sometimes two new edges and vertices), there is a permutational representation of the corresponding group. Group elements correspond to integer n-sequences and the nodes in the path generate all n! permutations. The extra node has a more complicated action, adding a certain quantity to some of the numbers.