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

Amílcar Sernadas, *Instituto Superior Técnico*

### Combining logic systems: Why, how, what for?

Motivated by applications in artificial intelligence and software
engineering that require the joint use of different deduction
formalisms, the interest in combination of logic systems has
recently been growing, but the topic is also of interest on purely
theoretical grounds. Several forms of combination have been
studied, like product, fusion, temporalization, parameterization,
synchronization and, more recently, fibring. In this guided tour of
the issues raised by the combination of logics, we define fibring
(the most general form of combination) in a very simple (yet
useful) context, discuss some examples and establish some
interesting transference results, namely preservation of strong
completeness and nonpreservation of congruence. We end the tour
with a brief reference to some open problems. The talk is based on
a recent overview paper (together with C. Sernadas) available
at
http://www.cs.math.ist.utl.pt/ftp/pub/SernadasA/03-SS-fiblog22.pdf
to appear in the CIM Bulletin.

### 04/11/2003, 15:00 — 16:00 — Room P3.10, Mathematics Building

Paulo Pinto, *Instituto Superior Técnico*

### Classification of Modular Invariants and Subfactors

### 21/10/2003, 15:00 — 16:00 — Room P3.10, Mathematics Building

Nara Jung, *Centro de Análise Matemática, Geometria e Sistemas Dinâmicos*

### Continuity properties of $\text{}{D}^{2}u$ in ${\mathrm{BV}}^{2}$ with strict convergence

### 14/10/2003, 15:00 — 16:00 — Room P3.10, Mathematics Building

Robert Oliver, *Université Paris 13*

### Homotopy equivalences between completed classifying spaces of
finite groups

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

João Paulo Santos, *Instituto Superior Técnico*

### Dirac operator, instantons and holomorphic bundles

### 30/09/2003, 15:00 — 16:00 — Room P3.10, Mathematics Building

Ana Paula Dias, *Universidade do Porto*

### Symmetry groupoids, synchrony, and coupled cell networks

### 23/09/2003, 15:00 — 16:00 — Room P3.10, Mathematics Building

Joana Ventura, *Instituto Superior Técnico*

### Homological algebra for the representation Green functor for
Abelian groups

### 09/09/2003, 15:00 — 16:00 — Room P3.10, Mathematics Building

Michael Grinfeld, *The University of Strathclyde in Glasgow*

### Multiplicity of periodic solutions in mean-field theories of
magnetisation

### 29/07/2003, 15:00 — 16:00 — Room P3.10, Mathematics Building

Leonardo Macarini, *IMPA, Rio de Janeiro*

### Hofer-Zehnder sensitive capacity of cotangent bundles and
symplectic submanifolds

We will consider a modified Hofer-Zehnder capacity sensitive to the
homotopy class of the periodic orbits and show that if a symplectic
manifold admits a free Hamiltonian circle action then it has
bounded Hofer-Zehnder (sensitive) capacity. We give two
applications of this result. Firstly, we prove that every closed
symplectic submanifold has a neighborhood with finite Hofer-Zehnder
capacity. Secondly, consider a closed manifold with an effective
circle action whose fixed point set has trivial normal bundle.
Then, its standard cotangent bundle has bounded Hofer-Zehnder
capacity.

### 22/07/2003, 15:00 — 16:00 — Room P3.10, Mathematics Building

Christian Wolf, *Wichita State University*

### Measures of maximal dimension for hyperbolic diffeomorphisms

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

Katrin Gelfert, *Max-Planck-Institut für Physik komplexer Systeme, Dresden*

### Dimension estimates in nonconformal dynamical systems

### 14/07/2003, 11:00 — 12:00 — Room P3.10, Mathematics Building

Maria José Pacífico, *Universidade Federal do Rio de Janeiro*

### Lorentz attractor versus singular hyperbolic attractor

### 08/07/2003, 15:00 — 16:00 — Room P3.10, Mathematics Building

Filippo Gazzola, *Universitá degli Studi del Piemonte Orientale*

### Existence and nonexistence results for anisotropic quasilinear
elliptic equations

### 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*

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

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

Waldyr Oliva, *CAMGSD and ISR - IST*

### Non-holonomic Systems and the Geometry of Constraints

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

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

### Flagelar Locomotion Via Geometric Mechanics

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

Matthew Perlmutter, *CAMGSD - IST*

### Gauged Poisson Structures

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

Giorgio Fusco, *Università degli Studi dell'Aquila*

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

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

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

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

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

David Kinderlehrer, *Carnegie Mellon University*

### 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.