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

该奖项将提供资金组织一次会议，“辛和泊松几何与代数，分析和拓扑学的相互作用”，庆祝辛和泊松几何出现四十年及其对数学主要领域的影响。会议的重点是辛几何和泊松几何的最新重要发展，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。会谈涉及的具体议题将包括：Taubes最近使用Seiberg-Witten理论证明的Weinstein猜想，拉格朗日相交理论的最新进展，经典和量子Yang-Baxter方程，Poisson和量子群胚，动态Weyl群，q-变形Casimir连接和Kazdhan-Lusztig函子。会议将提供一个论坛，概述最近发现的连接尼古拉Reshetikhin，圣武-Ngoc和其他可积系统之间的辛和代数几何和表示论。Reshetikhin和Vu-Ngoc会谈还将分别从更代数和更几何的角度讨论可积系统量子化的最新进展。其他议题涵盖的会议将考虑最近的突破有关测地流的本征函数，和Hitrik和Sjostrand的最近的工作谱的非自伴运营商在二维（这在很大程度上依赖于艾伦温斯坦的著名工作谱的Zoll表面）。Tudor Ratiu和Jerrold Marsden的演讲将集中在辛几何在物理和工程中的广泛应用，如流体和等离子体理论，液晶和微极流体。本次会议的目标是举办一个高规格的会议，汇集世界各地的专家和初级研究人员来讨论这些当前令人兴奋的相互作用。会议的时间（2010年5月）恰逢艾伦·温斯坦一周年？她从加州大学伯克利分校退休了。温斯坦是近四十年来辛几何和辛分析领域最有影响力的人物之一。他的基本工作启发了许多数学家，并导致发展的中心概念辛和泊松几何，以及建立辛几何作为一个独立的学科内的数学。这次会议将提供一个论坛，讨论温斯坦对几何和数学的影响。在过去的几十年里，辛几何、分析、低维拓扑和偏微分方程之间发生了许多引人注目的相互作用，从而使人们对数学的基本问题有了新的认识。今天辛几何是一个积极的，中央分支的数学人口的深刻的结果和连接与物理学，低维拓扑，规范理论，可积系统，表示论，群论，半经典分析和李群。会议的主题是阐明特定类型的相互作用的特点，在辛几何过去四十年的发展。 为此，会议将由初级和高级的领先专家进行会谈，描述这些领域中几个最基本的研究问题的当前状态。辛几何和泊松几何是现在已经建立的研究领域，它的语言和技术被用于数学，理论物理和工程的许多领域，如对称分叉问题，可积系统，弦理论，几何相位，非线性控制，非完整力学和机器人运动生成。

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.