Conference: Spectral Theory and Partial Differential Equations

会议：谱理论和偏微分方程

• 批准号: 1301620
• 负责人: Terence Tao
• 金额: $ 4万
• 依托单位: University of California-Los Angeles
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2013
• 资助国家: 美国
• 起止时间: 2013-04-01 至 2014-03-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1301620&HistoricalAwards=false
• 关键词: Conference; Spectral; Theory; Partial; Differential

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.

“会议：谱理论与偏微分方程”将于2013年6月17日至21日在加州大学洛杉矶分校举行。微局部分析是会议主题领域使用的主要工具之一，其根源可以追溯到20世纪初，但其系统发展始于大约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这门学科。例如，他们在找到椭圆算子的指标的Atiayh-Singer公式和解决关于椭圆算子在流形上的特征值分布的Weyl猜想方面发挥了决定性的作用，并为研究双曲方程在流形上的解的奇点传播提供了精确的工具。虽然微局部分析是线性偏微分方程理论的重要组成部分，但它也被成功地应用于非线性方程，并且微局部分析与光谱理论、散射理论和逆问题有许多联系。本次数学研究会议将汇集偏微分方程领域的顶尖专家，并将讨论微分方程中广泛的研究课题。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》系列丛书中专门出版会议上的演讲。将特别努力邀请研究生和博士后参加会议，从而激发未来数学家的研究。