One day miniworkshop on Variational Problems:Dynamics of Ginzburg-Landau vortices and critical points of the Kirchhoff functional.

Abstract:
 
For the two dimensional complex parabolic Ginzburg-Landau equation we prove that, asymptotically,  vortices evolve according to a simple ordinary differential equation, which is a gradient flow of the
Kirchhoff-Onsager functional. This convergence holds except for a finite number of times, corresponding to vortex collisions and splittings, which
we describe carefully. The only assumption is a natural energy bound on the initial data.

martedi' 13-06-2006 (16:00) - l'Aula Magna del Dipartimento
Cyrill Muratov :

"One day miniworkshop on Variational Problems". A Variational Approach to Front Propagation in Infinite Cylinders.

Abstract:

Gradient reaction-diffusion-advection systems arise in the context of modeling the kinetics of phase transitions, population dynamics and combustion. These systems are known to exhibit a variety of non-trivial spatio-temporal behaviors, most notably the
phenomenon of propagation and traveling waves. We introduce a variational formulation for the traveling wave solutions in cylindrical geometries with transverse potential flow, which allows us to
construct a certain class of traveling wave solutions and establish their monotonicity, asymptotic decay and, under some extra assumptions, uniqueness. These solutions are special in a sense that they are
characterized by a non-generic fast exponential decay ahead of the wave and play an important role in propagation phenomena for the initial value problem. We also construct an area-type functional
that gives a matching upper and lower bound for the propagation speed in the sharp reaction zone limit for weakly curved fronts.

ore 17.00 coffe-break

martedi' 13-06-2006 (17:30) - l'Aula Magna del Dipartimento "L. Tonelli"
Dorin Bucur :

"One day miniworkshop on Variational Problems". Shape analysis of the crack inverse problem

Abstract:

The talk deals with the identifiability of non-smooth defects  by boundary measurements, and the stability of their detection.  We extend
the result of Alessandrini and Valenzuela on the unique determination of a finite number of cracks or cavities by two boundary measurements, to
arbitrary closed sets satisfying quasi-everywhere a {\it conductivity assumption}. This new regularity concept is to be compared to the Wiener
criterion, rather than to the usual smoothness of the boundary. Relying on the geometric stability of the direct problem, we discuss  the stability of the inverse problem without imposing any a priori
boundary regularity of the unknown defects. As an application, we give a rigorous justification of the finite elements approximation of  the
defects.

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lunedi' 19-06-2006 (11:00) - Sala riunioni
Irinel Dragan (Dept. of Mathematics, Univ.of Texas at Arlington, USA) :

seminari congiunti col DIPART.MATEMATICA APPLICATA: On the Semivalues and the Shapley value for cooperative transferable utility games

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mercoledi' 21-06-2006 (15:00) - Sala dei Seminari
Jesus Ruiz (Universitad Complutense Madrid) :

Open questions concernings Hilbert's 17th Problem for analytic curves

Abstract
The Hilbert 17th Problem asks when a psd function is a sum of squares, and of how many.

For real analytic curves this reduces to the local problem
for germs at singular points. For those germs, the problem splits into the
consideration of their irreducible branches.

Now, irreducible curve germs are classically discussed
using the semigroup of values: all irreducible curves with fixed semigroup
form a "moduli" algebraic set in some finite dimensional affine space.

There, Pythagoras numbers, positive semidefinite germs, sum of squares
provide semialgebraic mappings on and stratifications of the "moduli" set.

The understanding od these semialgebraic data is a difficult matter that
has surprising connections with classical concepts (for instance, Arf
curves and Pythagorean curves are one and the same thing).

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