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01/07/2003, 15:00 — 16:00 — Room P3.10, Mathematics Building

Hermano Frid, *Instituto de Matemática Pura e Aplicada, Rio de Janeiro e Centro de Matemática e Aplicações Fundamentais*

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Soluções espacialmente periódicas para as
equações de Euler em dinâmica dos gases
relativística

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26/06/2003, 16:30 — 17:30 — Room P3.10, Mathematics Building

Waldyr Oliva, *CAMGSD and ISR - IST*

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Non-holonomic Systems and the Geometry of Constraints

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26/06/2003, 15:00 — 16:00 — Room P3.10, Mathematics Building

Jair Koiller, *Fundação Getúlio Vargas, Rio de Janeiro*

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Flagelar Locomotion Via Geometric Mechanics

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26/06/2003, 14:30 — 15:30 — Room P3.10, Mathematics Building

Matthew Perlmutter, *CAMGSD - IST*

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Gauged Poisson Structures

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26/06/2003, 11:00 — 12:00 — Room P3.10, Mathematics Building

Giorgio Fusco, *Università degli Studi dell'Aquila*

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Three Time Scales in the Steepest Descent Dynamics of a Regularized
Nonconvex Functional of the Gradient

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26/06/2003, 10:00 — 11:00 — Room P3.10, Mathematics Building

Piero Negrini, *Universitá di Roma I - La Sapienza*

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Integrability, Nonintegrability and Chaos in a System Related to
the Riemann Ellipsoid Problem

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23/06/2003, 15:00 — 16:00 — Room P3.10, Mathematics Building

David Kinderlehrer, *Carnegie Mellon University*

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Remarks about diffusion mediated transport

Typical flow regimes in aerodynamics and fluid dynamics involve
large Reynolds numbers. There are important issues regarding, for
example, the relationship between kinetic and potential energy or
turbulent behaviour. Here we shall discuss diffusion mediated
transport, a property of systems with quite small Reynolds numbers,
about 0.05. This is the environment of the living cell.
Diffusion mediated transport is implicated in the operation of
many molecular level systems. These include some liquid crystal and
lipid bilayer systems, and, especially, the motor proteins
responsible for eukaryotic cellular traffic. All of these systems
are extremely complex and involve subtle interactions on varying
scales. Earlier, we were interested in the design of material
microstructure, typically in order to optimize the performance of
devices that do work by changing their microstructure. In such
gadgets, like shape memory or magnetostrictive, energy transduction
is very close to equilibrium in order to minimize the energy budget
- think about remote controls. The chemical mechanical transduction
in motor proteins is, by contrast, quite distant from equilibrium.
These systems function in a dynamically metastable range.

We give a general dissipation principle and illustrate how it
may be used to describe transport, for example in flashing rachet
and conventional kinesin type motors. We introduce new methods
based on the Monge-Kantorovich problem and Wasserstein metric to
explore this. The equations we obtain are analogous to the ones
already formulated by Astumian, and Oster, Ermentrout, and Peskin,
and by Adjari and Prost and their collaborators. What is necessary
for transport? What is the role of diffusion? What is the role of
other elements of the system and how can dissipation be exploited
to understand this? How successful are we? The opportunity to
discover the interplay between chemistry and mechanics and to
elaborate the implications of metastability could not offer a more
exciting venue.

We are reporting here on joint work with Michel Chipot, Jean
Dolbeault, Stuart Hastings, and Michal Kowalczyk.

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17/06/2003, 15:00 — 16:00 — Room P3.10, Mathematics Building

Cristodor Ionescu, *Institute of Mathematics, Romanian Academy, Bucharest*

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Some remarks on evolutions

We present some result concerning evolutions of Noetherian local
rings of characteristic zero using Andre-Quillen homology of
commutative rings.

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12/06/2003, 11:00 — 12:00 — Room P3.10, Mathematics Building

Christopher Earles, *Rice University, Houston*

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Residue Theorems and Lie Algebroid Invariants

The recent work of Harvey and Lawson has resulted in a family of
residue theorems relating the singular sets (viewed as rectifiable
currents) of a vector bundle map to the Chern-Weil characteristic
forms of the bundles. Many of the classical singularity theorems
(e.g., the Argument Principle, the Poincare-Hopf Index Theorem, and
the Riemann-Roch Theorem) are special cases of these more general
formulae.
In this talk, I will review briefly the techniques used by
Harvey and Lawson and give an account of current work to extend
these to the study of Lie algebroids.

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03/06/2003, 15:00 — 16:00 — Room P3.10, Mathematics Building

Renato Iturriaga, *CIMAT, Guanajuato*

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Convergence of viscosity solutions of random Hamilton Jacobi
equations

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27/05/2003, 15:00 — 16:00 — Room P3.10, Mathematics Building

Miguel Rodríguez Olmos, *Instituto Superior Técnico*

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The topology of symplectic quotients for cotangent bundles

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20/05/2003, 15:00 — 16:00 — Room P3.10, Mathematics Building

Claudia Valls, *Università di Roma*

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Weak KAM Theory for multidimensional maps

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13/05/2003, 15:00 — 16:00 — Room P3.10, Mathematics Building

Gianluigi Del Magno, *Centro de Análise Matemática, Geometria e Sistemas Dinâmicos*

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Ergodic semifocusing billiards

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06/05/2003, 15:00 — 16:00 — Room P3.10, Mathematics Building

Rui Loja Fernandes, *Instituto Superior Técnico*

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Linearization of Poisson Brackets

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29/04/2003, 15:00 — 16:00 — Room P3.10, Mathematics Building

Luis Barreira, *Instituto Superior Técnico*

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Poincaré recurrence, geodesic flows, hyperbolic geometry

Today, we are arguably in possession of a satisfactory approach to
a quantitative description of recurrence. *As one knows well:
Poincaré only established that orbits return infinitely
often, not how often or when they return.*
This will be a colloquium type exposition of recent results that
shed new light on the subject, also discussing joint work with
Benoît Saussol, Christian Wolf, and Gianluigi Del Magno. The
talk will include the view of the (maybe classical) hyperbolic
geometer and briefly some consequences for number theory. No
prerequisites from dynamical systems or ergodic theory will be
necessary.

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08/04/2003, 15:00 — 16:00 — Room P3.10, Mathematics Building

Tanya Schmah, *University of Warwick*

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The local geometry of symmetric Hamiltonian systems on cotangent
bundles

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01/04/2003, 15:00 — 16:00 — Room P3.10, Mathematics Building

Jonathan Wattis, *University of Nottingham*

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A Coarse-graining approximation for the Becker-Doring equations

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25/03/2003, 15:00 — 16:00 — Room P3.10, Mathematics Building

Waldyr Oliva, *Centro de Análise Matemática, Geometria e Sistemas Dinâmicos e Instituto de Sistemas e Robótica*

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On the dimension and smoothness of attractors

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18/03/2003, 15:00 — 16:00 — Room P3.10, Mathematics Building

Alexei Davydov, *Vladimir State University, Russia*

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Optimal strategies of time averaged optimization of cyclic motion

We consider dynamic inequalities with locally bounded derivatives
on the circle and optimize the time averaged profit along
admissible motions which are defined for all nonegative time. We
describe the nature of optimal strategies, generic swichings
between them when the problem depends additionally from a one
dimensional parameter, and also the respective singularities of the
averaged profit like a function of the parameter.

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11/03/2003, 15:00 — 16:00 — Room P3.10, Mathematics Building

David Krejcirik, *Centro de Análise Matemática, Geometria e Sistemas Dinâmicos*

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Bound States in Curved Quantum Layers

We consider a nonrelativistic quantum particle constrained
to a curved hard-wall layer of constant width built over
a noncompact surface embedded in
${R}^{3}$.
Under the assumption that the surface curvatures vanish
at infinity, we find sufficient conditions which guarantee
the existence of geometrically induced bound states.