"Weyl Law at 100"

《韦尔定律100岁》

• 批准号: 1216660
• 负责人: Maciej Zworski
• 金额: $ 1.2万
• 依托单位: University of California-Berkeley
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2012
• 资助国家: 美国
• 起止时间: 2012-09-01 至 2013-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1216660&HistoricalAwards=false
• 关键词: Weyl; Law; 100

Abstract (Zworski, 1216660)This award provides funding to help defray the expenses of participants, especially women, graduate students, postdocs, and junior faculty, in the "The Weyl Law at 100" conference that will be held from September 19--22, 2012, at the Fields Institute for Research in Mathematical Sciences in Toronto, Canada. In 1912 Hermann Weyl published his paper establishing the Weyl law which gives the leading asymptotic description for the counting function of eigenvalues of the Dirichlet or Neumann Laplacian on a bounded domain in the Euclidean space. He later conjectured the form of the second term in asymptotics of the counting functions. After contributions by many mathematicians, among them, Courant, Hilbert, Agranovitch, Levitan, Hormander, Seeley, Duistermaat, Guillemin, Melrose and Sjostrand, the Weyl conjecture was solved by Ivrii in 1982. The workshop is intended as a forward-looking celebration of the 100th anniversary of Weyl's paper. Among the directions to be explored are the (conjectured) connection between random matrix theory and high energy distribution of differences between eigenvalues, probabilistic Weyl laws for non-self-adjoint operators, distribution of scattering resonances and fractal Weyl laws, and physical experiments related to quantum chaos and inverse problems. All of the conference topics are central to analysis and are extremely active areas of research. The conference will bring together a broad spectrum of accomplished researchers thereby providing ample opportunities to develop collaborative interactions, and the format of the meeting is such that young people will have ample opportunities to speak and be otherwise engaged in the various conference activities.

摘要（Zworski, 1216660）该奖项提供资金，帮助支付参加将于2012年9月19日至22日在加拿大多伦多菲尔兹数学科学研究所举行的“Weyl Law at 100”会议的参与者，特别是女性、研究生、博士后和初级教师的费用。1912年，Hermann Weyl发表了建立Weyl定律的论文，给出了欧几里得空间有界域上Dirichlet或Neumann Laplacian特征值计数函数的主要渐近描述。他后来推测了计数函数渐近中第二项的形式。在Courant、Hilbert、Agranovitch、Levitan、Hormander、Seeley、Duistermaat、Guillemin、Melrose和Sjostrand等许多数学家的贡献下，Weyl猜想于1982年由Ivrii解决。该研讨会旨在作为Weyl论文发表100周年的前瞻性庆祝活动。研究方向包括随机矩阵理论与特征值差的高能量分布之间的（推测）联系、非自伴随算子的概率Weyl定律、散射共振的分布和分形Weyl定律，以及与量子混沌和逆问题相关的物理实验。所有的会议主题都是分析的中心，也是非常活跃的研究领域。会议将汇集广泛的有成就的研究人员，从而为发展合作互动提供充足的机会，会议的形式是这样的，年轻人将有充足的机会发言，并以其他方式参与各种会议活动。