Emphasis Year in Algebraic and Smooth Microlocal Analysis

西北大学数学系计划在2011-12学年举办代数和光滑微局部分析重点年。这就需要在外地各级有一个不同期限的访客方案，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分析的。它是量子力学中半经典极限的数学基础，在物理和几何的其他领域也有应用。这项拟议的项目将把在从量子力学到表象理论、复杂几何学和镜面对称性等广泛不同背景下使用微局部方法的研究人员聚集在一起。强调年的主要特点是四个工作坊的计划，以及来自来访数学家的小型课程。讲习班的主题是：(1)代数微域分析(D-模和形变量化)；(2)解析微域分析(复数域中的微域分析)；(3)C无穷大背景下的光谱和散射理论；(4)非线性演化方程。这四个讲习班代表了相当不同的微局部分析领域，反映了西北大学实地集中的主要领域。分析微局部分析讲习班的目的是统一不同领域并将其联系起来。微局部分析的许多技术成就缺乏通俗易懂的论述，强调年应该有助于使许多领域的研究人员更容易获得微局部分析工具。微局部分析是分析和几何的一部分，根据空间的相空间研究函数、微分方程和其他对象。相空间的一个点描述了一个粒子在原始空间上的位置及其动量。特别是，它的尺寸是原来空间的两倍。相空间在经典和量子力学以及光学(如光线的空间)和物理学的其他部分中都扮演着基本的角色。相空间有更一般的类型，称为辛流形。特别是，大类的复流形，或不是基于实数而是基于复数的几何空间，都属于这一类。在辛流形和复流形之间还有其他不太为人所知的联系；它们由镜像对称来表示，这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到微分几何，再到复分析，再到数论，无处不在。西北大学重点年的目标是将在这些不同领域工作的领先研究人员聚集在一起。更多信息可以在website:http://www.math.northwestern.edu/~dbaskin/spscconf/上找到

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/