Emphasis Year in Algebraic and Smooth Microlocal Analysis

西北大学数学系计划在2011-12学年开设“代数与光滑微局部分析”重点年。这就需要制订一个在外地各级和不同期限访问的方案，并在一年中在外地举行四次会议。微局部分析是相空间的分析。它是支撑量子力学中半经典极限的数学，也应用于其他物理和几何领域。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局部方法，从量子力学到表征理论，复杂几何和镜像对称。强调年的中心特征是一个由四个讲习班组成的项目，以及来自访问数学家的迷你课程。讲习班的主题将是：(i)代数微局部分析（d模块和变形量化）；解析微局部分析（复域微局部分析）；c -∞环境下的光谱和散射理论；（iv）非线性演化方程。这四个讲习班代表了微局部分析的不同领域，反映了西北大学该领域的主要集中领域。分析微局部分析研讨会旨在统一和连接不同的领域。微局部分析的许多技术成就缺乏平易近人的说明，重点年应该有助于使许多领域的研究人员更容易获得微局部工具。微局部分析是分析和几何的一部分，它根据相空间研究空间上的函数、微分方程和其他物体。相空间的一个点描述了粒子在原始空间上的位置及其动量。特别是，它的维度是原始空间的两倍。相空间在经典力学和量子力学以及光学（如光线空间）和物理学的其他部分中起着基本作用。还有更一般的相空间类型，叫做辛流形。特别是，大的复流形，或者基于复数而非实数的几何空间，都在这门课中。辛流形和复流形之间还有其他一些鲜为人知的联系；它们通过镜像对称来表达，镜像对称是弦理论和几何的一个领域。所有这些都表明，微局部方法在数学和物理的许多领域发挥着至关重要的作用。事实上，这些领域从量子场论延伸到微分几何，从复分析到数论。西北大学重点年的目标是将这些不同领域的顶尖研究人员聚集在一起。更多信息请访问：http://www.math.northwestern.edu/~dbaskin/spscconf/

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/