Patterns In Mathematics par Anthony Joseph, Fulbert Mignot, Francois Murat, Bernard Prum, Rudolf Rentschler

First European Congress of Mathematics
par Anthony Joseph, Fulbert Mignot, Francois Murat, Bernard Prum, Rudolf Rentschler

Table of contents: Plenary Lectures • V.I. Arnold: The Vassiliev Theory of Discriminants and Knots • L. Babai: Transparent Proofs and Limits to Approximation • C. De Concini: Poisson Algebraic Groups and Representations of Quantum Groups at Roots of 1 • S.K. Donaldson: Gauge Theory and Four-Manifold Topology • W. Müller: Spectral Theory and Geometry • D. Mumford: Pattern Theory: A Unifying Perspective • A.-S. Sznitman: Brownian Motion and Obstacles • M. Vergne: Geometric Quantization and Equivariant Cohomology • Parallel Lectures • Z. Adamowicz: The Power of Exponentiation in Arithmetic • A. Björner: Subspace Arrangements • B. Bojanov: Optimal Recovery of Functions and Integrals • J.-M. Bony: Existence globale et diffusion pour les modèles discrets • R.E. Borcherds: Sporadic Groups and String Theory • J. Bourgain: A Harmonic Analysis Approach to Problems in Nonlinear Partial Differatial Equations • F. Catanese: (Some) Old and New Results on Algebraic Surfaces • Ch. Deninger: Evidence for a Cohomological Approach to Analytic Number Theory • S. Dostoglou and D.A. Salamon: Cauchy-Riemann Operators, Self-Duality, and the Spectral Flow

Chromatikon 4
par Michel Weber

Le réseau « Chromatiques whiteheadiennes » a pour objectif premier de fédérer les recherches sur les différents aspects, nuances et implications de la pensée du philosophe et algébriste britannique Alfred North Whitehead (1861-1947). C’est dans ce cadre qu’ont été créés en 2002 à l’Université Paris 1 Panthéon Sorbonne des séminaires de recherche sur la philosophie organique whiteheadienne. L’ « Annuaire de la philosophie en procès » publie les principaux résultats de ces travaux et offre complémentairement des études critiques et des comptes rendus récents dans les domaines whiteheadiens et connexes.

The « Chromatiques whiteheadiennes » network intends to bring together research on the different aspects, nuances and implications of Alfred North Whitehead’s (1861-1947) thought. Since 2002, the network has fostered in Paris 1 Panthéon Sorbonne research seminars on his organic philosophy. The Chromatikon yearbook publishes the main results of this work and also offer critical studies and reviews in Whiteheadian and related fields. The Chromatikon yearbooks are complementary to the works published in ontos’ « Chromatiques whiteheadiennes » and« Process Thought » series.

The Algebra of Metaphysics
par Ronny Desmet, Michel Weber

Drawing upon the major Harvard works — Science and the Modern
World (1925), Process and Reality (1929) and Adventures
of Ideas (1933) —, the essays gathered here on the occasion
of the creation of the Applied Process Metaphysics Summer
Institute seek, first, to introduce into Whitehead’s thought by
clarifying what is at stake in his philosophy and by providing a
synoptic vision of his key categories in light of their historical
development and, second, to foster a creative dialogue among
all participants. These essays give the opportunity to travel
through most aspects of Whitehead’s legacy: anthropology,
ecology, education, epistemology, metaphysics, psychology,
political theory and relativity physics.

Fields Medallists’ Lectures
par Michael Francis Atiyah, Daniel Iagolnitzer

Although the Fields Medal does not have the same public recognition as the Nobel Prizes, they share a similar intellectual standing. It is restricted to one field that of mathematics and an age limit of 40 has become an accepted tradition. Mathematics has in the main been interpreted as pure mathematics, and this is not so unreasonable since major contributions in some applied areas can be (and have been) recognized with Nobel Prizes. The restriction to 40 years is of marginal significance, since most mathematicians have made their mark long before this age.

A list of Fields Medallists and their contributions provides a bird’s eye view of mathematics over the past 60 years. It highlights the areas in which, at various times, greatest progress has been made. This volume does not pretend to be comprehensive, nor is it a historical document. On the other hand, it presents contributions from 22 Fields Medallists and so provides a highly interesting and varied picture.

The contributions themselves represent the choice of the individual Medallists. In some cases the articles relate directly to the work for which the Fields Medals were awarded. In other cases new articles have been produced which relate to more current interests of the Medallists. This indicates that while Fields Medallists must be under 40 at the time of the award, their mathematical development goes well past this age. In fact the age limit of 40 was chosen so that young mathematicians would be encouraged in their future work.

The Fields Medallists’ Lectures is now available on CD-ROM. Sections can be accessed at the touch of a button, and similar topics grouped together using advanced keyword searches.