Emphasis Year in Algebraic and Smooth Microlocal Analysis

代数和平滑微局部分析的重点年份

• 批准号: 1137706
• 负责人: Jared Wunsch
• 金额: $ 6万
• 依托单位: Northwestern University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2011
• 资助国家: 美国
• 起止时间: 2011-09-01 至 2013-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1137706&HistoricalAwards=false
• 关键词: Emphasis; Year; Algebraic; Smooth; Microlocal

The Department of Mathematics at Northwestern University plans to hold an emphasis year in Algebraic and Smooth Microlocal Analysis in the 2011-12 academic year. This entails having a program of visitors in the field at all levels and for varying durations and holding four conferences in the field during the course of the year. Microlocal analysis is analysis in phase space. It is the mathematics underpinning the semi-classical limit in quantum mechanics, as well as having applications in other areas of physics and geometry. The proposed project would bring together researchers using microlocal methods in widely disparate contexts, ranging from quantum mechanics to representation theory, complex geometry, and mirror symmetry. The central feature of the emphasis year is to be a program of four workshops, as well as mini-courses from visiting mathematicians. The topics of the workshops will be: (i) Algebraic Microlocal Analysis (D-modules and deformation quantization); (ii) Analytic Microlocal Analysis (microlocal analysis in the complex domain); (iii) Spectral and Scattering theory in the C-infinity setting; (iv) Nonlinear Evolution Equations. These four workshops represent quite distinct areas of microlocal analysis, reflecting the major areas of concentration in the field at Northwestern. The workshop on Analytic Microlocal Analysis is intended to unify and bridge the different areas. Many of the technical triumphs in microlocal analysis lack approachable expositions, and the emphasis year should help make microlocal tools more accessible to researchers in many fields.Microlocal Analysis is a part of analysis and geometry that studies functions, differential equations, and other objects on a space in terms of its phase space. A point of the phase space describes a position of a particle on the original space together with its momentum. In particular, its dimension is double that of the original space. The phase space plays a fundamental role in classical and quantum mechanics, as well as in optics (as the space of light rays) and other parts of physics. There are more general types of phase spaces, called symplectic manifolds. In particular, large classes of complex manifolds, or geometric spaces based not on real but on complex numbers, are in this class. There are other, less well-understood, connections between symplectic manifolds and complex manifolds; they are expressed by the mirror symmetry, an area of both string theory and geometry. All this suggests that microlocal methods play crucial role in many areas of mathematics and physics. In fact these areas spread all the way from quantum field theory to differential geometry to complex analysis to number theory. The goal of the Emphasis Year at Northwestern is to bring together leading researchers working in these different areas.More information can be found on the website:http://www.math.northwestern.edu/~dbaskin/spscconf/

西北大学数学系计划在2011-12学年举办代数学和光滑微局部分析的重点年。 这就需要制定一个各级和不同期限的外地访问者方案，并在一年中在外地举行四次会议。 微局部分析是在相空间中进行的分析。 它是量子力学中半经典极限的数学基础，也在物理学和几何学的其他领域有应用。 拟议中的项目将把研究人员聚集在一起，在广泛不同的背景下使用微观方法，从量子力学到表象理论，复杂几何和镜像对称。 重点年的中心特点是四个讲习班的计划，以及访问数学家的迷你课程。 讲习班的主题是：㈠代数微局部分析（D-模块和变形量化）; ㈡解析微局部分析（复域中的微局部分析）; ㈢ C-无限环境中的谱和散射理论; ㈣非线性演化方程。这四个研讨会代表了微观分析的不同领域，反映了西北大学该领域的主要集中领域。微观分析研讨会旨在统一和弥合不同的领域。 微局部分析中的许多技术成果缺乏平易近人的阐述，重点年应该有助于使微局部工具更容易为许多领域的研究人员所用。微局部分析是分析和几何的一部分，它研究函数，微分方程和空间上的其他对象。相空间中的一点描述了粒子在原始空间中的位置及其动量。特别是，它的尺寸是原始空间的两倍。相空间在经典力学和量子力学、光学（如光线空间）和物理学的其他部分中起着重要作用。相空间有更一般的类型，称为辛流形。特别是，大类的复流形，或几何空间的基础上，而不是真实的，但复数，是在这一类。辛流形和复流形之间还有其他不太清楚的联系，它们可以用镜像对称来表示，这是弦理论和几何学的一个领域。这些都表明微局部方法在数学和物理的许多领域中起着至关重要的作用。事实上，这些领域从量子场论到微分几何，再到复分析，再到数论。 在西北重点年的目标是汇集在这些不同领域工作的领先研究人员。更多信息可以在网站上找到：http://www.math.northwestern.edu/~dbaskin/spscconf/