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

中西部PDE研讨会是一个系列会议，自1977年以来每两年在中西部的大学举行一次。偏微分方程(PDE)在整个科学和工程中无处不在，因为它们表达了感兴趣的量的变化率之间的关系。线性偏微分方程组，如拉普拉斯方程、热方程、波动方程和薛定谔方程，是物理学中许多现象的中心。非线性偏微分方程组产生于广义相对论、凝聚态物理和光学、规范场理论和流体力学等领域。非线性偏微分方程组也被用来处理几何分析领域的数学问题。这次会议汇集了来自这些领域的专家，以交流最新研究成果的信息，并促进合作研究。该奖项为将于2014年5月10日至11日周末在西北大学举行的第73届中西部PDE研讨会提供部分支持。拉普拉斯方程、热方程、波动方程和薛定谔方程的研究仍然是一个活跃而丰富的课题；例如，在紧致和非紧致环境(谱和散射理论)下的拉普拉斯本征函数和本征值的研究是当前相当感兴趣的。此外，在广义相对论(爱因斯坦方程)、凝聚态物理和光学(非线性薛定谔方程)、规范场理论(杨-米尔斯方程)和流体(纳维斯托克斯方程和欧拉方程)中出现的非线性偏微分方程组仍然充满神秘色彩。在几何方面，赋予特殊度量的黎曼流形的研究在最近几年取得了惊人的进展。涉及哈密尔顿的Ricci流的工作和Fano流形上的Kähler-Einstein度规理论的突破性发展涉及到来自PDE的深刻的新工具。这些理论分别与一个非线性退化抛物型方程(Ricci流)和一个椭圆型方程(复Monge-Ampère)联系在一起。本次研讨会的讨论将涉及这些主题和其他主题。大会鼓励和支持初级数学家、妇女和代表不足的少数群体广泛和多样化的参与。大会网址：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/