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11/12/2001, 15:00 — 16:00 — Room P3.10, Mathematics Building

Paul Norbury, *Adelaide University, Australia*

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Integrable systems and geometry

Holomorphic functions can be useful when studying many natural nonlinear differential equations. Two examples are nonlinear magnetic monopoles and the nonlinear KdV equation that describes solitary water waves. The rich structure of complex analysis makes this a powerful tool whenever it can be applied. More specifically, a meromorphic function can be uniquely determined by very little information, say knowledge of its poles and residues. This can sometimes enable us to deduce many features, including explicit solutions, of a nonlinear differential equation.

This talk will give an introductory account of these ideas. It is hoped that the talk contains something for both novices and experts in the field.

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04/12/2001, 15:00 — 16:00 — Room P3.10, Mathematics Building

Luis Barreira, *Instituto Superior Técnico*

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Recorrência de Poincaré, dinâmica hiperbólica e fracções contínuas

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20/11/2001, 15:00 — 16:00 — Room P3.10, Mathematics Building

Michael Paluch, *Instituto Superior Técnico*

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Spectral sequences, pairings and twisted products

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13/11/2001, 15:00 — 16:00 — Room P3.10, Mathematics Building

Jorge Silva, *Instituto Superior Técnico*

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Conjugação de Operadores Pseudo-Diferenciais por Operadores Integrais de Fourier

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08/11/2001, 11:00 — 12:00 — Room P3.10, Mathematics Building

Bastien Fernandez, *Centre de Physique Théorique, CNRS, Luminy*

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Dynamics of two coupled unimodal maps

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05/11/2001, 14:30 — 15:30 — Room P3.10, Mathematics Building

David E. Evans, *Cardiff University*

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The irrational rotation algebra

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23/10/2001, 15:00 — 16:00 — Room P3.10, Mathematics Building

Gyula Farkas, *Centro de Análise Matemática, Geometria e Sistemas Dinâmicos*

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Discretizing delay equations with small delay

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18/10/2001, 11:00 — 12:00 — Room P3.10, Mathematics Building

Luís Silva, *Universidade de Évora*

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Famílias de aplicações unidimensionais com descontinuidades

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09/10/2001, 15:00 — 16:00 — Room P3.10, Mathematics Building

José Natário, *Instituto Superior Técnico*

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Linking and causality

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25/09/2001, 15:00 — 16:00 — Room P3.10, Mathematics Building

João Palhoto de Matos, *Instituto Superior Técnico*

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(Des)igualdades entre médias no interior e na fronteira

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18/09/2001, 15:00 — 16:00 — Room P3.10, Mathematics Building

Bernard Dacorogna, *Ecole Polytechnique Fédérale, Lausanne*

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On the existence and regularity of solutions of $\mathrm{du}=f$

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13/09/2001, 16:00 — 17:00 — Room P3.10, Mathematics Building

Melanie Bertelson, *Max-Planck Institut für Mathematik, Bonn*

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Regular Poisson manifolds and their foliations

A regular Poisson manifold can be described as a foliated space supporting a tangentially symplectic form. As was discussed in a previous talk, such forms are solutions of a certain partial differential relation that can be shown to satisfy the h-principle when some natural condition on the underlying foliated space, namely that of being *uniformly open* is fulfilled. Examples of foliations will be presented in this talk that are not induced by any Poisson structure although the basic obstructions vanish. In particular, these foliated spaces are not uniformly open.

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13/09/2001, 14:30 — 15:30 — Room P3.10, Mathematics Building

Pierre Bielavski, *Université Libre de Bruxelles*

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Non formal deformation quantizations and Lie group actions

I will present a few aspects of *convergent* star product theory involving star representation techniques. The main goal is to define a class of non-commutative differential manifolds via explicit universal deformation formulae for (non-Abelian) group actions on Fréchet algebras. In the examples considered here, these formulae will be of two types: oscillatory integral and analytic. The first kind may be interpreted as finite dimensional versions of Cattaneo-Felder's formulae for Kontsevich star products on symplectic manifolds in presence of curvature. The second kind is based on deformations of Gelfand-Shilov's spaces of type S. Analytic continuations of those yield non-commutative (Fréchet) function algebras containing observables with exponential growth, unlike in the (topological) ${C}^{*}$ framework. The methods used to produce these formulae comes from symmetric spaces and harmonic analysis on Lie groups.

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26/07/2001, 11:00 — 12:00 — Room P3.10, Mathematics Building

Andrea Brini, *Università degli Studi di Bologna*

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An introduction to topological methods in the theory of posets II. The Möbius function as an Euler characteristic

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24/07/2001, 15:00 — 16:00 — Room P3.10, Mathematics Building

Andrea Brini, *Università degli Studi di Bologna*

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An introduction to topological methods in the theory of posets I. Galois connections and a theorem of Quillen

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19/07/2001, 11:00 — 12:00 — Room P3.10, Mathematics Building

Paulo Lima-Filho, *Texas A&M University*

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Intersection products in algebraic geometry

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17/07/2001, 15:00 — 16:00 — Room P3.10, Mathematics Building

Juan-Pablo Ortega, *École Polytechnique Fédérale de Lausanne*

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Singular dual pairs and optimal momentum maps

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13/07/2001, 11:00 — 12:00 — Room P3.10, Mathematics Building

Roger Plymen, *University of Manchester*

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Noncommutative geometry and number theory III

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12/07/2001, 11:00 — 12:00 — Room P3.10, Mathematics Building

Roger Plymen, *University of Manchester*

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Noncommutative geometry and number theory II