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Abordagem probabilística a sistemas dinâmicos de dimensão finita e infinita




One task is devoted to hydrodynamics: we do not try to introduce random noise in Euler or Navier-Stokes equations, but regard the second one as a stochastic deformation of the first equation, whose predictions should be, therefore, intrinsically probabilistic. We use the Lagrangian stochastic flows and show that the analysis of Euler equation à la Arnold can be deformed, in the same sense, when the fluid is viscous.

Another topic is centered on integrable dynamical systems and their geometry: detailed analysis of specific classical integrable systems as well as deformation of such ideas and techniques along the trajectories of diffusion processes with tools of Geometric Mechanics.

The third topic, Chern-Simons Gauge theory, includes a study from a probabilistic viewpoint. In the old tradition of Quantum Field Theory, a symbolic Feynman path integral has been the origin of an amazing number of rich geometrical consequences.

The host institution is the Group of Mathematical Physics of the University of Lisbon. This is a research centre in Mathematics funded by the Portuguese Science Foundation (FCT) which has always been awarded the highest possible classification in all international evaluations carried out by FCT; in the latest of these (2008) only 6 research units out of a total universe of 20 Maths Centres in the whole country received this classification.

The project includes funding for two additional postdoctoral positions starting before the end of 2011. For a description of the conditions, deadlines, etc, please see the call for applications.

Time span: 01/01/2010-31/12/2012
Funding institution: FCT
Budget: € 122261.00

Algumas publicações relevantes

(poderá ver informação sobre outras publicações dos investigadores envolvidos, consultando as respectivas páginas)

F. Cipriano e A. B. Cruzeiro
Navier-Stokes equation and diffusions on the group of diffeomorphisms of the torus
Commun. Math. Phys. 275 (2007), 255-269
V. Dragovic e M. Radnovic
Hyperelliptic Jacobians as billiard algebra of pencils of quadrics: beyond Poncelet porisms
Advances in Math. 219 (2008), 1577-1607
P. Lescot e J.-C. Zambrini
Probabilistic deformation of contact geometry, diffusion processes and their quadratures
Progress in Probab. Birkhäuser 59 (2007), 203-226
A. Hahn
Chern-Simons models on S²×S¹, torus gauge fixing and link invariants II
J. Geom. Phys. 58 (2008), 1124-1136