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The first European Congress of Mathematics was held in Paris from
July 6 to July 10, 1992, at the Sorbonne and Pantheon-Sorbonne
universities. It was hoped that the Congress would constitute a
symbol of the development of the community of European nations.
More than 1,300 persons attended the Congress. The purpose of the
Congress was twofold. On the one hand, there was a scientific facet
which consisted of forty-nine invited mathematical lectures that
were intended to establish the state of the art in the various
branches of pure and applied mathematics. This scientific facet
also included poster sessions where participants had the
opportunity of presenting their work. Furthermore, twenty-four
specialized meetings were held before and after the Congress. The
second facet of the Congress was more original. It consisted of six
teen round tables whose aim was to review the prospects for the
interactions of mathematics, not only with other sciences, but also
with society and in particular with education, European policy and
industry. In connection with this second goal, the Congress also
succeeded in bring ing mathematics to a broader public. In addition
to the round tables specific ally devoted to this question, there
was a mini-festival of mathematical films and two mathematical
exhibits. Moreover, a Junior Mathematical Congress was organized,
in parallel with the Congress, which brought together two hundred
high school students."
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. Muller:
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. Bjorner: Subspace Arrangements *
B. Bojanov: Optimal Recovery of Functions and Integrals * J.-M.
Bony: Existence globale et diffusion pour les modeles 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
Table of Contents: D. Duffie: Martingales, Arbitrage, and Portfolio
Choice * J. Frohlich: Mathematical Aspects of the Quantum Hall
Effect * M. Giaquinta: Analytic and Geometric Aspects of
Variational Problems for Vector Valued Mappings * U. Hamenstadt:
Harmonic Measures for Leafwise Elliptic Operators Along Foliations
* M. Kontsevich: Feynman Diagrams and Low-Dimensional Topology *
S.B. Kuksin: KAM-Theory for Partial Differential Equations * M.
Laczkovich: Paradoxical Decompositions: A Survey of Recent Results
* J.-F. Le Gall: A Path-Valued Markov Process and its Connections
with Partial Differential Equations * I. Madsen: The Cyclotomic
Trace in Algebraic K-Theory * A.S. Merkurjev: Algebraic K-Theory
and Galois Cohomology * J. Nekovar: Values of L-Functions and
p-Adic Cohomology * Y.A. Neretin: Mantles, Trains and
Representations of Infinite Dimensional Groups * M.A. Nowak: The
Evolutionary Dynamics of HIV Infections * R. Piene: On the
Enumeration of Algebraic Curves - from Circles to Instantons * A.
Quarteroni: Mathematical Aspects of Domain Decomposition Methods *
A. Schrijver: Paths in Graphs and Curves on Surfaces * B.
Silverman: Function Estimation and Functional Data Analysis * V.
Strassen: Algebra and Complexity * P. Tukia: Generalizations of
Fuchsian and Kleinian Groups * C. Viterbo: Properties of Embedded
Lagrange Manifolds * D. Voiculescu: Alternative Entropies in
Operator Algebras * M. Wodzicki : Algebraic K-Theory and Functional
Analysis * D. Zagier: Values of Zeta Functions and Their
Applications
The first European Congress of Mathematics was held in Paris from
July 6 to July 10, 1992, at the Sorbonne and Pantheon-Sorbonne
universities. It was hoped that the Congress would constitute a
symbol of the development of the community of European nations.
More than 1,300 persons attended the Congress. The purpose of the
Congress was twofold. On the one hand, there was a scientific facet
which consisted of forty-nine invited mathematical lectures that
were intended to establish the state of the art in the various
branches of pure and applied mathematics. This scientific facet
also included poster sessions where participants had the
opportunity of presenting their work. Furthermore, twenty four
specialized meetings were held before and after the Congress. The
second facet of the Congress was more original. It consisted of
sixteen round tables whose aim was to review the prospects for the
interactions of mathe matics, not only with other sciences, but
also with society and in particular with education, European policy
and industry. In connection with this second goal, the Congress
also succeeded in bringing mathematics to a broader public. In
addition to the round tables specifically devoted to this question,
there was a mini-festival of mathematical films and two
mathematical exhibits. Moreover, a Junior Mathematical Congress was
organized, in parallel with the Congress, which brought together
two hundred high school students."
The first European Congress of Mathematics was held in Paris from
July 6 to July 10, 1992, at the Sorbonne and Pantheon-Sorbonne
universities. It was hoped that the Congress would constitute a
symbol of the development of the community of European nations.
More than 1,300 persons attended the Congress. The purpose of the
Congress was twofold. On the one hand, there was a scientific facet
which consisted of forty-nine invited mathematical lectures that
were intended to establish the state of the art in the various
branches of pure and applied mathematics. This scientific facet
also included poster sessions where participants had the
opportunity of presenting their work. Furthermore, twenty four
specialized meetings were held before and after the Congress. The
second facet of the Congress was more original. It consisted of
sixteen round tables whose aim was to review the prospects for the
interactions of mathe matics, not only with other sciences, but
also with society and in particular with education, European policy
and industry. In connection with this second goal, the Congress
also succeeded in bringing mathematics to a broader public. In
addition to the round tables specifically devoted to this question,
there was a mini-festival of mathematical films and two
mathematical exhibits. Moreover, a Junior Mathematical Congress was
organized, in parallel with the Congress, which brought together
two hundred high school students."
Table of Contents: D. Duffie: Martingales, Arbitrage, and Portfolio
Choice * J. Frohlich: Mathematical Aspects of the Quantum Hall
Effect * M. Giaquinta: Analytic and Geometric Aspects of
Variational Problems for Vector Valued Mappings * U. Hamenstadt:
Harmonic Measures for Leafwise Elliptic Operators Along Foliations
* M. Kontsevich: Feynman Diagrams and Low-Dimensional Topology *
S.B. Kuksin: KAM-Theory for Partial Differential Equations * M.
Laczkovich: Paradoxical Decompositions: A Survey of Recent Results
* J.-F. Le Gall: A Path-Valued Markov Process and its Connections
with Partial Differential Equations * I. Madsen: The Cyclotomic
Trace in Algebraic K-Theory * A.S. Merkurjev: Algebraic K-Theory
and Galois Cohomology * J. Nekovar: Values of L-Functions and
p-Adic Cohomology * Y.A. Neretin: Mantles, Trains and
Representations of Infinite Dimensional Groups * M.A. Nowak: The
Evolutionary Dynamics of HIV Infections * R. Piene: On the
Enumeration of Algebraic Curves - from Circles to Instantons * A.
Quarteroni: Mathematical Aspects of Domain Decomposition Methods *
A. Schrijver: Paths in Graphs and Curves on Surfaces * B.
Silverman: Function Estimation and Functional Data Analysis * V.
Strassen: Algebra and Complexity * P. Tukia: Generalizations of
Fuchsian and Kleinian Groups * C. Viterbo: Properties of Embedded
Lagrange Manifolds * D. Voiculescu: Alternative Entropies in
Operator Algebras * M. Wodzicki : Algebraic K-Theory and Functional
Analysis * D. Zagier: Values of Zeta Functions and Their
Applications
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. Muller:
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. Bjorner: Subspace Arrangements *
B. Bojanov: Optimal Recovery of Functions and Integrals * J.-M.
Bony: Existence globale et diffusion pour les modeles 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
In many domains one encounters "systems" of interacting elements,
elements that interact more forcefully the closer they may be. The
historical example upon which the theory offered in this book is
based is that of magnetization as it is described by the Ising
model. At the vertices of a regular lattice of sites, atoms "choos
e" an orientation under the influence of the orientations of the
neighboring atoms. But other examples are known, in physics (the
theories of gasses, fluids, .. J, in biology (cells are
increasingly likely to become malignant when their neighboring
cells are malignant), or in medecine (the spread of contagious
deseases, geogenetics, .. .), even in the social sciences (spread
of behavioral traits within a population). Beyond the spacial
aspect that is related to the idea of "neighboring" sites, the
models for all these phenomena exhibit three common features: - The
unavoidable ignorance about the totality of the phenomenon that is
being studied and the presence of a great number of often
unsuspected factors that are always unquantified lead inevitably to
stochastic models. The concept of accident is very often inherent
to the very nature of the phenomena considered, so, to justify this
procedure, one has recourse to the physicist's principle of
indeterminacy, or, for example, to the factor of chance in the
Mendelian genetics of phenotypes.
In many domains one encounters "systems" of interacting elements,
elements that interact more forcefully the closer they may be. The
historical example upon which the theory offered in this book is
based is that of magnetization as it is described by the Ising
model. At the vertices of a regular lattice of sites, atoms "choos
e" an orientation under the influence of the orientations of the
neighboring atoms. But other examples are known, in physics (the
theories of gasses, fluids, .. J, in biology (cells are
increasingly likely to become malignant when their neighboring
cells are malignant), or in medecine (the spread of contagious
deseases, geogenetics, .. .), even in the social sciences (spread
of behavioral traits within a population). Beyond the spacial
aspect that is related to the idea of "neighboring" sites, the
models for all these phenomena exhibit three common features: - The
unavoidable ignorance about the totality of the phenomenon that is
being studied and the presence of a great number of often
unsuspected factors that are always unquantified lead inevitably to
stochastic models. The concept of accident is very often inherent
to the very nature of the phenomena considered, so, to justify this
procedure, one has recourse to the physicist's principle of
indeterminacy, or, for example, to the factor of chance in the
Mendelian genetics of phenotypes.
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