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

美国国家科学基金提案dms -0308970摘要项目：Joceline Lega，亚利桑那大学题目：美国菲尔兹研究所2003/2004特别年度青年数学家该奖项将资助美国年轻的数学研究人员参加2003-2004学年秋季在菲尔兹研究所进行的一个为期一学期的椭圆和抛物型偏微分方程（PDE）专题项目。本学期将会有一些重点活动，包括两个为期一周的关于PDE当前主题的研讨会：一个是关于“变分法：超导性，材料微观结构和几何问题”的研讨会，将于2003年8月25日至30日举行，另一个是关于“物理模式”的研讨会，计划于2003年11月14日至18日举行。其他具体活动包括一系列关于流体动力学数学问题的迷你课程，以及一到两个周末的专题讨论会，重点讨论当前感兴趣的专题。PDE理论是数学与其他研究领域相互作用的中心点，它与其他科学学科有许多联系。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。PDE的进步在许多其他科学学科的现代发展中起着重要的作用，值得注意的是，它实际上重新配置了应用数学、数学物理和微分几何的许多领域。菲尔兹研究所的这个项目旨在关注“椭圆型和抛物型偏微分方程的当前问题”，主要是应用数学、数学物理和/或微分几何所激发的领域。椭圆型和抛物型偏微分方程理论出现在物理科学的许多问题中，包括超导材料的结构，连续介质中的相变，新应用的新材料的微观结构，以及各种物理系统中图案形成的建模。在这一领域有广泛的杰出和活跃的国际研究人员，其中相当一部分人将参加菲尔兹研究所2003年秋季专题学期。参加该项目的年轻美国研究人员将有很多机会与其他学科、政府科学实验室和工业界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.