Conference on Thermodynamic Formalism: Dynamical Systems, Statistical Properties, and Their Applications

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This award is for support of the participation of US mathematicians, mainly early career researchers, at the Jean-Morlet Chair Conference on Thermodynamic Formalism: Dynamical Systems, Statistical Properties and their Applications at Centre International de Recontres Mathematiques (CIRM) in Luminy from December 9 until December 13, 2019. This conference will bring together many internationally leading researchers in ergodic theory and dynamical systems and will have a special focus on recent developments in the application of thermodynamic formalism to dynamics. Up to 20 US mathematicians will be supported by this grant and will learn of recent progress and novel techniques in modern dynamical systems theory. In addition to the formal lectures there will be plenty of time for discussions to foster new collaborations and maximize interactions between participants. The interactions with international colleagues will lead to collaborations and new research directions which will benefit US researchers, their PhD students and their home institutions.Ideas from statistical mechanics in the guise of thermodynamic formalism were introduced into the study of dynamical systems by Sinai and Ruelle in the late 1960s. The notions of pressure, equilibrium states and entropy among others were successfully applied to classify and study the statistical and geometric properties of hyperbolic dynamical systems. This conference will continue this theme and focus on several topics that are very active and fruitful, including: studying statistical properties using transfer operators and anisotropic Banach spaces; the structure and properties of Gibbs measures; moduli spaces, flows and applications to number theory; fractal geometry and dimension theory. The conference website is at https://www.chairejeanmorlet.com/2019-2-pollicott-vaienti.htmlThis award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.