73rd Midwest PDE Seminar, May 10-11, 2014

中西部PDE研讨会是自1977年以来在中西部大学每两年举行一次的系列会议。偏微分方程（PDE）在科学和工程中无处不在，因为它们表达了兴趣量的变化率之间的关系。线性偏微分方程，如拉普拉斯、热、波和Schrödinger方程是许多物理现象的核心。非线性偏微分方程出现在广义相对论、凝聚态物理和光学、规范场理论和流体动力学等领域。非线性偏微分方程也被用来解决几何分析领域的数学问题。本次会议汇集了来自这些领域的专家，交流有关最新研究成果的信息并促进合作研究。该奖项为第73届中西部PDE研讨会提供部分支持，该研讨会将于2014年5月10日至11日在西北大学举行。对拉普拉斯、热、波和Schrödinger方程的研究仍然是一个生动而丰富的课题；例如，研究拉普拉斯特征函数和特征值在紧凑和非紧凑设置（光谱和散射理论）是相当大的兴趣。此外，广义相对论（爱因斯坦方程）、凝聚态物理和光学（非线性Schrödinger方程）、规范场论（杨-米尔斯方程）和流体（纳维-斯托克斯和欧拉方程）中出现的非线性偏微分方程仍然充满奥秘。在几何方面，对具有特殊度量的黎曼流形的研究近年来取得了惊人的进展。涉及汉密尔顿的利玛奇流和Fano流形上Kähler-Einstein度量理论的突破性发展的工作涉及来自PDE的深刻的新工具。这些理论分别与非线性退化抛物方程（里奇流）和椭圆方程（复蒙日-安普瑞）联系在一起。本次研讨会将讨论这些和其他主题。会议鼓励并支持初级数学家、女性和未被充分代表的少数群体广泛而多样的参与。会议网址：http://www.math.northwestern.edu/midwestpde/

The Midwest PDE Seminar is a conference series that has been held biannually since 1977 at universities across the Midwest. Partial Differential Equations (PDE) are ubiquitous throughout science and engineering, since they express relationships between rates of change of quantities of interest. Linear PDE such as Laplace, heat, wave, and Schrödinger equations are central to many phenomena in physics. Nonlinear PDE arise in fields such as general relativity, condensed matter physics and optics, gauge field theory, and fluid dynamics. Nonlinear PDE are also employed to tackle mathematical problems in the area of geometric analysis. This meeting brings together experts from across these fields to exchange information about recent research results and to foster collaborative research.This award provides partial support for the 73rd edition of the Midwest PDE Seminar, to be held at Northwestern University on the weekend of May 10-11, 2014. Study of the Laplace, heat, wave, and Schrödinger equations remains a lively and rich subject; for instance the study of Laplace eigenfunctions and eigenvalues in both compact and noncompact settings (spectral and scattering theory) is of considerable current interest. Moreover, nonlinear PDE such as arise in general relativity (Einstein equations), condensed matter physics and optics (nonlinear Schrödinger equation), gauge field theory (Yang-Mills equations), and fluids (Navier-Stokes and Euler equations) remain rich in mysteries. On the side of geometry, the study of Riemannian manifolds endowed with special metrics has seen astounding advances in recent years. Work involving Hamilton's Ricci flow and breaking developments in the theory of Kähler-Einstein metrics on Fano manifolds have involved profound new tools from PDE. These theories are tied to a nonlinear degenerate parabolic equation (Ricci flow) and an elliptic equation (complex Monge-Ampère) respectively. Discussions in this seminar will address these and other topics. The conference encourages and supports broad and diverse participation of junior mathematicians, women, and underrepresented minorities.Conference web site: http://www.math.northwestern.edu/midwestpde/