Support for US Participants at CIRM, March 13-17, 2017 Conference: Scattering, Resonances and Dynamics

“共振：几何散射和动力学”研讨会于3月13日至17日在法国鲁米尼的国际协调数学中心(CIRM)举行，将聚集研究共振几何理论(谱几何、表示理论、调和分析、微局域分析、解析数论、数学物理、微局域分析、量子动力学、几何散射理论)不同方面的研究人员以及来自不同国家的博士生和初级研究人员。它的目的是展示和讨论关于共振的几何方面和动力学的最新结果，分享观点和想法，并加强或促进互动。会议将为博士生和年轻科学家提供机会，与一些与共振相关的领域的知名研究人员见面，并与他们交流想法。为了让参与者能够接触到更专业的演讲，一些专家将进行辅导和调查演讲。此外，两个下午将专门用于初级参与者的演讲。这将使博士生和博士后有机会展示他们的工作，这是进入研究世界和建立科学合作的关键一步。共振的概念被引入量子力学来研究系统的亚稳态，即系统只有在足够强的干扰下才偏离的长寿命状态。在数学上，共振要么表现为经典哈密顿量量子化的离散本征值，要么表现为经典流的转移算符的本征值。他们的研究最初针对R^n上的薛定谔算子，后来扩展到更几何的情形。由于它们在不同的物理环境中发挥的作用，在过去的几年里，在理解几何以及经典和量子共振的分析方面取得了相当大的进展。尽管如此，许多重要和基本的问题仍然悬而未决。由于共振的非自伴性，许多阻止使用经典论点的困难出现了。此外，在几何情形下，当(局部)对称空间的秩大于1时，所知甚少。通过几种不同的方法，利用调和分析和表示理论，或微局部分析和散射理论的技术，如复标度，已经取得了部分进展。因此，要研究高维和高阶几何情形中的共振，需要不同数学界的共同努力，年轻的研究人员应该与该理论各个方面的专家接触，以取得重大进展。大会网页列表：http://scientific-events.weebly.com/1604.html

The workshop "Resonances: Geometric Scattering and Dynamics," taking place at the Centre International de Recontres Mathématiques (CIRM) in Luminy, France, from March 13 to 17, will gather researchers working on the different aspects of the geometric theory of resonances (spectral geometry, representation theory, harmonic analysis, microlocal analysis, analytic number theory, mathematical physics, microlocal analysis, quantum dynamics, geometric scattering theory) as well as Ph. D. students and junior researchers from different countries. Its objectives are to present and discuss the latest results on the geometric aspects and dynamics of resonances, share points of view and ideas, and to strengthen or promote interactions. The conference will give Ph.D. students and young scientists the opportunity to meet some of the prominent researchers in the fields related to resonances and to exchange ideas with them. To make the more specialized talks accessible to the participants, some experts will give tutorial and survey talks. Moreover, two afternoons will be devoted to talks of junior participants. This will give the Ph.D. students and the postdocs the possibility of presenting their work, which is an essential step for entering in the world of research and for building scientific collaborations. The notion of resonance was introduced in quantum mechanics to study metastable states of a system, that is long-lived states from which the system deviates only with sufficiently strong disturbances. Mathematically, resonances appear either as discrete eigenvalues of the quantization of a classical Hamiltonian or as the eigenvalues of the transfer operator of the classical flow. Their study, initially aimed at Schroedinger operators on R^n, was extended to more geometric situations. Because of the role they play in various physical contexts there has been a considerable progress in understanding the geometry and the analysis of classical and quantum resonances in the last years. Nevertheless, many important and basic questions are still open. Many difficulties preventing to use classical arguments arise because of the non-self-adjoint nature of resonances. Also, in the geometric case of (locally) symmetric spaces, very little is known when the rank of the spaces is bigger than 1. Partial advances have been obtained, with several different approaches, using either harmonic analysis and representation theory, or microlocal analysis and techniques from scattering theory such as complex scaling. To study resonances in higher dimensional and higher rank geometric situations, a joint effort of different mathematical communities is therefore needed, and young researchers should have contacts with experts from the various aspects of the theory to make significant progress. The webpage listing of the conference: http://scientific-events.weebly.com/1604.html