Workshop on Spectral Invariants on Non-Compact and Singular Spaces

非紧空间和奇异空间谱不变量研讨会

• 批准号: 1219405
• 负责人: Pierre Albin
• 金额: $ 1.76万
• 依托单位: University of Illinois at Urbana-Champaign
• 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: 2012-05-15 至 2013-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1219405&HistoricalAwards=false
• 关键词: Workshop; Spectral; Invariants; Non; Compact

This summer, during July 23-27, 2012, there will be a workshopentitled ``Spectral invariants on non-compact and singular spaces"held at the Centre de Recherches Mathematiques (CRM) in Montreal,Canada. Important examples of spectral invariants are given by theindex of an elliptic operator, the determinant of the Laplacian on aRiemannian manifold, the eta invariant (or spectral asymmetry) of aself-adjoint elliptic operator, and the analytic torsion. Onnon-compact or singular manifolds, the very definition of spectralinvariants is much more delicate. The workshop will highlight recentdevelopments and new research directions in spectral geometry insingular contexts (e.g., spectral invariants in the presence of cuspsand edges, scattering theory for asymptotically regular non-compactgeometries, applications to moduli spaces and geometric structures,etc.).This award provides funding to defray the expenses of U.S.participants at this conference. The expected participants represent abalanced mixture of senior and junior researchers and include some ofthe most renowned experts on spectral invariants. This is a veryactive field with many recent developments, and this workshop willprovide an important forum to advertise the state-of-the-art and anexcellent opportunity for collaboration. The webpage for theconference can be found at:http://www.crm.umontreal.ca/act/theme/theme_2012_2_en/invariants12_e.php

今年夏天，2012 年 7 月 23 日至 27 日期间，将在加拿大蒙特利尔数学研究中心 (CRM) 举办题为“非紧奇异空间上的谱不变量”的研讨会。谱不变量的重要例子由椭圆算子的索引、黎曼流形上的拉普拉斯行列式、eta 不变量给出。 自伴椭圆算子（或谱不对称性）和解析挠率。在非紧或奇异流形上，谱不变量的定义要微妙得多。 研讨会将重点介绍奇异背景下谱几何的最新发展和新研究方向（例如，尖点和边缘存在下的谱不变量、渐近的散射理论） 常规非紧几何、模空间和几何结构的应用等）。该奖项提供资金来支付美国与会者参加本次会议的费用。预期的参与者由高级和初级研究人员组成，其中包括一些最著名的光谱不变量专家。这是一个非常活跃的领域，最近有许多发展，本次研讨会将提供一个重要的论坛来宣传该领域 最先进的技术和绝佳的合作机会。会议网页位于：http://www.crm.umontreal.ca/act/theme/theme_2012_2_en/invariants12_e.php