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The theory of Toeplitz operators has come to resemble more and more in recent years the classical theory of pseudodifferential operators. For instance, Toeplitz operators possess a symbolic calculus analogous to the usual symbolic calculus, and by symbolic means one can construct parametrices for Toeplitz operators and create new Toeplitz operators out of old ones by functional operations.

If P is a self-adjoint pseudodifferential operator on a compact manifold with an elliptic symbol that is of order greater than zero, then it has a discrete spectrum. Also, it is well known...

Over the last decade, spin glass theory has turned from a fascinating part of t- oretical physics to a ?ourishing and rapidly growing subject of probability theory as well. These developments have been triggered to a large part by the mathem- ical understanding gained on the fascinating and previously mysterious "Parisi solution" of the Sherrington-Kirkpatrick mean ?eld model of spin glasses, due to the work of Guerra, Talagrand, and others. At the same time, new aspects and applications of the methods developed there have come up. The presentvolumecollects a number of reviewsaswellas...

Proceedings of the Brasov Conference, Poiana Brasov 1989, Romania

This volume contains the proceedings of the First Ukrainian-French Romanian School "Algebraic and Geometric Methods in Mathematical Physics," held in Kaciveli, Crimea (Ukraine) from 1 September ti1114 September 1993. The School was organized by the generous support of the Ministry of Research and Space of France (MRE), the Academy of Sciences of Ukraine (ANU), the French National Center for Scientific Research (CNRS) and the State Committee for Science and Technologies of Ukraine (GKNT). Members of the International Scientific Committee were: J.-M. Bony (paris), A. Boutet de Monvel-Berthier...

CONTENTS: L. Boutet de Monvel: Indice de systemesdifferentiels.- C. De Concini, C. Procesi: Quantum groups.-P. Schapira, J.P. Schneiders: Index theorems forR-constructible sheaves and for D-modules.- N. Berline, M.Vergne: The equivariant Chern character and index ofG-invariant operators.

This volume contains the proceedings of the First Ukrainian-French- Romanian School "Algebraic and Geometric Methods in Mathematical Physics", held in Kaciveli, Crimea (Ukraine) from 1 September ti1114 September 1993. The School was organized by the generous support of the Ministry of Research and Space of France (MRE), the Academy of Sciences of Ukraine (ANU), the French National Center for Scientific Research (CNRS) and the State Committee for Science and Technologies of Ukraine (GKNT). Members of the International Scientific Committee were: J.-M. Bony (paris), A. Boutet de Monvel-Berthier...

Jacques Bros has greatly advanced our present understanding of rigorous quantum field theory through numerous fundamental contributions. The impact of his work is also visible in several articles in this book. Quantum fields are considered as genuine mathematical objects, whose various properties and relevant physical interpretations have to be studied in a well-defined mathematical framework.

Key topics: Analytic structures of QFT, renormalization group methods, gauge QFT, stability properties and extension of the axiomatic framework, QFT on models of curved spacetimes, QFT on...