Symplectic and Poisson Geometry in interaction with Algebra, Analysis and Topology

辛几何和泊松几何与代数、分析和拓扑的相互作用

• 批准号: 0965738
• 负责人: Maciej Zworski
• 金额: $ 3.8万
• 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: 2010
• 资助国家: 美国
• 起止时间: 2010-03-01 至 2011-02-28
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0965738&HistoricalAwards=false
• 关键词: Symplectic; Poisson; Geometry; interaction; Algebra

This award will provide funding to organize a conference,``Symplectic and Poisson geometry in interaction with Algebra, Analysis and Topology'', celebrating four decades since the emergence of symplectic and Poisson geometry and their influence on major areas of mathematics. The conference focuses on recent important developments in symplectic and Poisson geometry, and the interactions of these fields with Analysis, Algebra, differential equations and low-dimensional topology. Specific topics covered by the talks will include: Taubes' recent proof of the Weinstein conjecture using Seiberg-Witten theory, recent progress in Lagrangian intersection theory, classical and quantum Yang-Baxter equations, Poisson and quantum groupoids, dynamical Weyl groups, q-deformed Casimir connections and Kazdhan-Lusztig functors. The conference will provide a forum to outline the recently found connections by Nicolai Reshetikhin, San Vu-Ngoc and others between integrable systems in symplectic and algebraic geometry and representation theory. Reshetikhin and Vu-Ngoc talks will also discuss the recent progress in the quantization of integrable systems from a more algebraic and a more geometric view point, respectively. Other topics covered in the conference will regard recent breakthroughs in relating geodesic flow to eigenfunctions, and Hitrik and Sjostrand's recent work on spectra of non-self adjoint operators in dimension two (which relies heavily on Alan Weinstein's famous work on spectra of Zoll surfaces). The talks by Tudor Ratiu and Jerrold Marsden will focus on applications of symplectic geometry to a wide problems in physics and engineering such as as fluid and plasma theory, liquid crystals and micropolar fluids.The goal behind this conference is that of holding a high profile meeting to bring together world experts and junior researchers to discuss these current exciting interactions. The time of the conference (May 2010) coincides with the first year anniversary of Alan Weinstein?s retirement from UC Berkeley. Weinstein has been one of the most influential figures in symplectic geometry and analysis in the past forty years. His fundamental work has inspired many mathematicians and led to the development of central concepts in symplectic and Poisson geometry, as well as to the establishment of symplectic geometry as an independent discipline within mathematics. The conference will provide a forum to dicuss Weinstein's impact on geometry and mathematics at large. The last few decades have witnessed numerous spectacular interactions between symplectic geometry, analysis, low dimensional topology and partial differential equations leading to new understanding in fundamental problems of mathematics. Today symplectic geometry is an active, central branch of mathematics populated by deep results and connections with physics, low-dimensional topology, gauge theory, integrable systems, representation theory, group theory, semiclassical analysis and Lie groups. The main theme of the Conference is to illuminate the particular type of interactions which characterize the past forty years of developments in symplectic geometry. To this end the conference will have talks by leading experts, both junior and senior, describing the current state of the art of several of the most fundamental research problems in these areas. Symplectic and Poisson geometry are by now well established fields of research, and its language and techniques are being used in many areas of mathematics, theoretical physics, and engineering such as symmetric bifurcation problems, integrable systems, string theory, geometric phases, nonlinear control, nonholonomic mechanics and locomotion generation in robotics.

该奖项将为组织会议提供资金``与代数，分析和拓扑互动的符号和泊松几何形状''''''自从出现自symplectic和Poisson几何形状及其对主要数学领域的影响以来，庆祝了四十年。会议的重点是符号和泊松几何形状的最新重要发展，以及这些领域与分析，代数，微分方程和低维拓扑的相互作用。演讲所涵盖的具体主题将包括：使用Seiberg-Witten理论，Lagrangian交叉路口理论的最新进展，经典和量子阳边的方程，Poisson和Quantum groupers，动态Weyl群，Q-DENEFFormical casimir Connections以及Kazdhan-Lusztig functors。该会议将提供一个论坛，概述Nicolai Reshetikhin，San Vu-Ngoc以及其他在符号和代数的几何学和代表理论中的连接。 Reshetikhin和Vu-ngoc谈话还将分别讨论来自更代数和更几何观点的可集成系统量化的最新进展。会议中涵盖的其他主题将考虑到将大地测量流与本征函数联系起来的最新突破，以及Hitrik和Sjostrand最近在Dimension二的非自我伴随运营商光谱的工作（这很大程度上依赖Alan Weinstein在Zoll表面上的著名作品）。 Tudor Ratiu和Jerrold Marsden的对话将集中在象征性几何形状上的应用中，例如液体和等离子体理论，例如流体和等离子体理论，液晶和微极性流体。会议（2010年5月）的时间与艾伦·温斯坦（Alan Weinstein）从加州大学伯克利分校（UC Berkeley）退休的一周年纪念日相吻合。在过去的四十年中，温斯坦一直是符号几何和分析中最有影响力的数字之一。他的基本工作激发了许多数学家的启发，并导致了象征性和泊松几何形状的中心概念的发展，以及建立符号几何形状作为数学中的独立学科。会议将为Dicuss Weinstein对整个几何和数学的影响提供一个论坛。在过去的几十年中，见证了符号几何形状，分析，低维拓扑和偏微分方程之间的许多壮观相互作用，从而导致了数学基本问题的新理解。如今，符合性几何形状是数学的一个积极的中心分支，这些数学是由深度结果和与物理学，低维拓扑，量规理论，可集成系统，表示理论，群体理论，半经典分析和谎言组的联系所填充的。会议的主要主题是阐明特定类型的互动类型，这些相互作用是过去40年的象征性几何发展的特征。 为此，会议将由初级和高级专家的领先专家进行谈判，描述了这些领域几项最基本研究问题的现行状况。符合性和泊松几何形状现在已经建立了良好的研究领域，其语言和技术正在用于数学，理论物理学和工程等许多领域，例如对称分化问题，可集成的系统，弦乐理论，几何学，几何相，非线性控制，非线性控制，非外观机械师和毕业生机械师和毕业生局的生成。