This grant is to provide travel support for American participants of two Workshops organized as part of a semester-long program "Hyperbolic Dynamics, Large Deviations and Fluctuations" that takes place at the Centre Interfacultaire Bernoulli, Ecole Politechnique, Lausanne, Switzerland, March-June 2013. The first workshop is on "Large deviations and thermodynamical formalism" and the second one is on "Limit Theorems for dynamical systems". Each workshop is preceded by a series of intensive mini-courses for post-graduate and post-doctoral students given by distinguished mathematicians in the field of dynamical systems.
During the last 50 years statistical properties of dynamical systems have been a center of extensive study in dynamics with many great applications to other areas of mathematics as well as outside to physics, engineering and biology. The systematic study of statistical properties began in the early 60's with the works of Sinai and Ruelle, and later of Bowen, who laid the foundations of thermodynamics. Though the methods they developed were of rather general nature, their applications were restricted mostly to uniformly hyperbolic systems. Much wider horizons were opened after the development of non-uniform hyperbolicity theory that is also known as "Pesin's theory". The main activities in dynamics these days are concentrated around studying non-uniformly hyperbolic systems, hyperbolic systems with singularities, and more generally, systems which posses some kind of hyperbolicity however do not belong to the previously mentioned categories. The main aim of the program is to bring together leading experts and young researchers working on statistical properties of dynamical systems and their applications in statistical mechanics, and mathematical physics as well as to foster scholarly exchange and collaboration. The workshops are intended to provide a focus of activities and a meeting place for mathematicians from various countries working in dynamical systems and related topics. They will serve as a forum for both young and established researchers to exchange ideas with their counterparts throughout the world, promote current and future research and create a concrete agenda for further research on several fronts. All participants, including members of traditionally underrepresented groups will also benefit from the presence of many strong young mathematicians from Europe.
" and "Large deviations and thermodynamical formalis" were part of a semester-long program "Hyperbolic Dynamics, Large Deviations and Fluctuations" that took place at the Centre Interfacultaire Bernoulli, EPF Lausanne, Switzerland in Spring 2013; -- "Dynamical Systems and Geometry", Marseille -- Lumini, France, March 2014; -- "Houston Summer School on Dynamical Systems", Houston, TX, May 2014; -- "Probability in Dynamics", Rio-de-Janeiro, Brazil, May 2014. During the last 50 years statistical properties of dynamical systems of various types and in many different situations have been a subject of extensive study in statistical mechanics and thermodynamics, ergodic and probability theories, and some areas of mathematical physics. The results of this study have had a profound effect on a whole lot of areas in mathematics, physics, engineering and biology. Intellectual Merit: The school-conferences provided a plethora of activities and a meeting place for mathematicians from around the globe working in dynamical systems and related topics. They were also a forum for both young and established researchers to exchange ideas with their counterparts throughout the world. The mini-courses were given by distinguished mathematicians, well-known experts in the field of dynamical systems. Thus, these events promoted current and future research and created a concrete agenda for further research on several fronts. Broader Impact. The school-conferences were focused on the development and support of young mathematicians who learned and interacted directly with leading researchers and were also exposed to discuss and collaborate with distinguished participants. All participants, including members of traditionally underrepresented groups benefited highly from the presence of many strong young mathematicians from Europe and Latin America.
