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

为 2017 年 3 月 13 日至 17 日 CIRM 会议上的美国参与者提供支持：散射、共振和动力学

• 批准号: 1700044
• 负责人: Tomasz Przebinda
• 金额: $ 1.44万
• 依托单位: University of Oklahoma Norman Campus
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2017
• 资助国家: 美国
• 起止时间: 2017-03-01 至 2018-02-28
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1700044&HistoricalAwards=false
• 关键词: Support; US; Participants; CIRM; March

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

工作坊“共鸣：几何散射与动力学，"发生在中心国际Luminy数学Recontres(这个),法国,从3月13日到17日,将收集的研究人员在共振的几何理论的不同方面(光谱几何、表象理论、谐波分析、微局部分析,解析数论、数学物理、微局部分析,量子力学,几何散射理论)以及博士和初级研究人员来自不同国家的学生。其目标是展示和讨论共振几何方面和动力学的最新成果，分享观点和想法，并加强或促进相互作用。会议将为博士生和年轻科学家提供机会，与共振相关领域的一些杰出研究人员会面，并与他们交流思想。为了使更专业的讲座对与会者更容易理解，一些专家将进行指导和调查讲座。此外，将有两个下午专门用于青年与会者的会谈。这将使博士生和博士后有机会展示他们的工作，这是进入研究领域和建立科学合作的重要一步。共振的概念是在量子力学中引入来研究系统的亚稳态的，亚稳态是指只有在足够强的扰动下系统才会偏离的长寿命状态。在数学上，共振要么表现为经典哈密顿量的量化的离散特征值，要么表现为经典流的传递算子的特征值。他们的研究最初是针对R^n上的薛定谔算子，后来扩展到更多的几何情况。由于它们在各种物理环境中所起的作用，在过去的几年里，在理解几何和分析经典共振和量子共振方面取得了相当大的进展。然而，许多重要和基本的问题仍然悬而未决。由于共振的非自伴随性质，阻碍使用经典论证的许多困难出现了。同样，在（局部）对称空间的几何情况下，当空间的秩大于1时，我们知道的很少。利用谐波分析和表征理论、微局部分析和散射理论（如复标度）等不同的方法，已经取得了部分进展。因此，研究高维高阶几何情况下的共振需要不同数学界的共同努力，年轻的研究人员需要与理论各方面的专家进行接触，才能取得重大进展。会议网页列表：http://scientific-events.weebly.com/1604.html