Conference: Spectral Theory and Partial Differential Equations

“会议：谱理论和偏微分方程”将于2013年6月17日至21日在加州大学洛杉矶分校举行。微观局部分析是会议主题领域的主要工具之一，其根源可以追溯到20世纪初，但其系统的发展始于大约50年前的伪微分算子和傅立叶积分算子理论。 从那时起，这些理论彻底改变了偏微分方程的主题。例如，他们发挥了决定性的作用，发现阿蒂亚-辛格公式指数的椭圆算子和解决外尔猜想分布的特征值椭圆算子流形上，他们提供了精确的工具，需要研究传播的奇异性的解决方案的双曲方程流形。虽然微局部分析一直是线性偏微分方程理论的重要组成部分，它也已成功地应用于非线性方程，以及有许多连接的微局部分析的频谱理论，散射理论，和逆问题。这次数学研究会议将汇集领先的专家在偏微分方程，它将考虑各种各样的研究课题在微分方程。这次会议将增加来自不同专业的数学家之间的交流，并将加速几个领域的研究进展。组织者计划在美国数学学会出版的当代数学系列的专用卷中发表会议上提出的谈话。特别努力将使研究生和博士后研究员的会议，从而刺激未来的数学家的研究。

The ``Conference: Spectral Theory and Partial Differential Equations'' will be held June 17-21, 2013 at the University of California-Los Angeles. The roots of microlocal analysis,one of the main tools employed in the conference subject area, go back to the beginning of the twentieth century, but its systematic development began about fifty years ago with the theories of Pseudodifferential Operators and Fourier Integral Operators. Since then these theories have revolutionized the subject of partial differential equations. For example, they have played decisive roles in finding the Atiayh-Singer formula for the index of an elliptic operator and in solving the Weyl conjecture about the distribution of eigenvalues for elliptic operators on manifolds, and they provided the precise tools needed for studying the propagation of singularities for solutions of hyperbolic equations on manifolds. Though microlocal analysis has been an important part of linear PDE theory, it has also been successfully applied to non-linear equations as well and there are numerous connections of microlocal analysis to spectral theory, scattering theory, and inverse problems.This mathematics research conference will bring together leading experts in partial differential equations and it will consider a wide variety of research topics in differential equations. The conference will increase communication among mathematicians from different specialties and it will accelerate research progress in several fields. The organizers plan to publish the talks presented on the conference in a dedicated volume of the series Contemporary Mathematics published by the American Mathematical Society. Special efforts will be made to bring graduate students and postdoctoral fellows to the conference and thereby to stimulate the research of future mathematicians.