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

该奖项是为了支持美国数学家，主要是早期职业研究人员，参加2019年12月9日至12月13日在Luminy举行的Jean-Morlet热力学形式主义主席会议：动力系统，统计特性及其应用。这次会议将汇集许多国际领先的研究人员在遍历理论和动力系统，并将有一个特别关注的热力学形式主义的动态应用的最新发展。多达20名美国数学家将获得这笔赠款的支持，并将了解现代动力系统理论的最新进展和新技术。除了正式的讲座，将有足够的时间进行讨论，以促进新的合作，并最大限度地提高参与者之间的互动。 与国际同行的互动将导致合作和新的研究方向，这将有利于美国的研究人员，他们的博士生和他们的家乡机构。从统计力学的想法在热力学形式主义的幌子被引入到动力系统的研究西奈和Ruelle在20世纪60年代末。压力、平衡态和熵等概念被成功地应用于双曲动力系统的统计和几何性质的分类和研究。本次会议将继续这一主题，并集中在几个非常活跃和富有成果的主题，包括：使用转移算子和各向异性Banach空间研究统计性质;吉布斯测度的结构和性质;模空间，流和数论应用;分形几何和维数理论。会议网站是https://www.chairejeanmorlet.com/2019-2-pollicott-vaienti.htmlThis奖反映了NSF的法定使命，并已被认为值得通过使用基金会的知识价值和更广泛的影响审查标准进行评估的支持。

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.