Junior US- Based Mathematicians at 03/04 Special Yr At Fields Institute

NSF提案摘要DMS-0308970PI：亚利桑那大学Joceline Lega题目：2003/2004学年菲尔兹学院特别年度的美国初级数学家该奖项将提供支持，使年轻的美国数学研究人员能够参加为期一学期的椭圆和抛物型偏微分方程(PDE)主题项目，该项目将于2003-2004学年秋季在菲尔兹学院举行。在本学期中，将有几个重点活动期，包括两个为期一周的关于PDE当前主题的工作坊：一个是2003年8月25-30日举行的“变分演算：超导电性、材料微结构和几何问题”工作坊，另一个是定于2003年11月14-18日举行的“物理学中的模式”工作坊。其他具体活动包括关于流体力学数学问题的一系列迷你课程，以及为期一到两个周末的专题讨论会。偏微分方程理论是数学与其他研究领域互动的中心点，它与其他科学学科的联系方式有很多种。近几十年来，该领域取得了许多重大进展，是一个非常活跃和充满活力的研究领域。偏微分方程的进展在许多其他科学学科的现代发展中起到了重要作用，值得注意的是，它实际上改变了应用数学、数学物理和微分几何的许多领域。菲尔兹研究所的这一项目主要针对应用数学、数学物理和/或微分几何领域的“椭圆型和抛物型偏微分方程组的当前问题”。椭圆和抛物线偏微分方程组的理论出现在许多物理科学问题中，包括超导材料的结构，连续介质中的相变，新材料的微结构应用，以及各种物理系统中图案形成的模拟。该领域有广泛的国际知名和活跃的研究人员，其中许多人将参加2003年秋季菲尔兹研究所的专题学期。参加该项目的年轻美国研究人员将找到许多机会，与在其他学科、政府科学实验室和工业领域工作的数学分析师和研究人员进行富有成效的合作。组委会将努力发挥这些互动的潜力。

ABSTRACT of NSF proposal DMS-0308970PI: Joceline Lega, University of ArizonaTitle: Junior US-Based Mathematicians at 2003/2004 Special Year at Fields InstituteThis award will provide support to enable young US mathematical researchers to participate in a semester long thematic program in elliptic and parabolic partial differential equations (PDE) to take place at the Fields Institute during the autumn of the academic year 2003-2004. During the semester there will be a number of focused periods of activity, including two one-week long workshops on current topics in PDE: one will be a workshop on the "Calculus of Variations: Superconductivity, Microstructure of Materials and Geometric Problems" to take place August 25 - 30, 2003 and the other will be a workshop on "Patterns in Physics" scheduled for November 14 - 18, 2003. Additional specific activities include a mini-course series of lectures on mathematical problems in fluid dynamics as well as one or two weekend-long symposia focused on specialized topics of current interest.The theory of PDE is a center-point where mathematics interacts with other areas of research, and there are many ways in which it has ties with other scientific disciplines. In the recent several decades the field has seen numerous major advances, and it is a very active and vibrant area of research. Progress in PDE has been important in the modern development of a number of other scientific subjects, and notably it has virtually reconfigured many areas of applied mathematics, mathematical physics and differential geometry. This program at the Fields Institute intends to focus on "current problemsin elliptic and parabolic PDE", principally in areas that are motivated by applied mathematics, mathematical physics and/or differential geometry. The theory of elliptic and parabolic PDE arises in numerous problems in the physical sciences, including the structure of superconducting materials, phase transitions in continuous media, the microstructure of new materials for novel applications, and the modeling of pattern formation in a large variety of physical systems. There is a broad international spectrum of prominent and active researchers in the field, a notable number of whom will be participating in the Fall 2003 thematic semester at the Fields Institute. Young US based researchers attending this program will find many opportunities for fruitful collaboration with mathematical analysts and researchers working in other academic disciplines, in government scientific laboratories as well as in industry. The organizing committees will make efforts to bring out the potential for these interactions.