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

该奖项旨在支持美国数学家（主要是早期职业研究人员）参加于2019年12月9日至12月13日在Luminy国际数学中心（CIRM）举行的热力学形式主义：动力系统，统计性质及其应用Jean-Morlet主席会议。本次会议将汇集许多国际领先的遍历理论和动力系统的研究人员，并将特别关注热力学形式论在动力学中的应用的最新发展。多达20名美国数学家将得到这项资助，并将学习现代动力系统理论的最新进展和新技术。除了正式的讲座外，还将有大量的时间进行讨论，以促进新的合作并最大限度地提高参与者之间的互动。与国际同事的互动将导致合作和新的研究方向，这将有利于美国研究人员，他们的博士生和他们的家乡机构。在热力学形式主义的幌子下，统计力学的思想在20世纪60年代末被西奈和鲁埃尔引入到动力系统的研究中。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，重点讨论几个非常活跃和富有成果的主题，包括：利用转移算子和各向异性巴拿赫空间研究统计性质；吉布斯测度的结构和性质；模空间、模流及其在数论中的应用分形几何与维数理论。该会议的网站是https://www.chairejeanmorlet.com/2019-2-pollicott-vaienti.htmlThis。该奖项反映了美国国家科学基金会的法定使命，并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，被认为值得支持。

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.