May 11 -15, 2015
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The main objective of this workshop is to make advances on the analysis of systems with multiple time scales and the interplay between the deterministic and stochastic aspects of such systems. Such a theory is important in a variety of engineering and scientific applications with multiple time scales, including climate modelling, meteorology, molecular dynamics and non-equilibrium statistical mechanics. The importance is due to the reduction from a generally high dimensional setting to a lower dimensional system incorporating only the slowest modes.
Whereas averaging leads to a lower dimensional deterministic system, fluctuations from averaging and homogenization leads to a lower dimensional stochastic differential equation. Classically, the starting equations have been taken to be stochastic and there is a well-developed theory of averaging and homogenization for such systems. However, the same types of results arise from deterministic chaos. In the case of homogenization, there are interesting connections with the longstanding question of smooth approximation of stochastic integrals (after Wong-Zakai) and links with Lyons’ theory of rough paths. The current situation is that three related strands of research (i) averaging and homogenization for stochastic systems, (ii) averaging and fluctuations from averaging in deterministic systems, and (iii) homogenization for deterministic systems, have been developing separately. The purpose of the proposed workshop is to share ideas and promote interaction between these three strands, leading to significant advances. Hence we aim at bringing together international experts from both stochastic analysis and dynamical systems, to share and advance the state of knowledge concerning multiscale systems. Also we intend to have several young participants to facilitate the input of new energies in this exciting field of research. |
Scientific & Organizing Committee
Carlangelo Liverani (University of Rome) Speakers
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