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

NSF提案DMS-0308970 PI摘要：Joceline Lega，亚利桑那大学标题：菲尔兹研究所2003/2004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一个学期的椭圆和抛物偏微分方程（PDE）专题计划。2003-2004学年秋季在菲尔兹研究所举行。在学期中，将有一些集中的活动时间，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、材料的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，另一个研讨会将于11月14日至18日举行，2003.其他具体活动包括一个小型课程系列讲座在流体动力学的数学问题，以及一个或两个周末的专题讨论会集中在当前感兴趣的专业主题。PDE理论是一个中心点，数学与其他研究领域的互动，有很多方式，它与其他科学学科的联系。在最近的几十年里，该领域取得了许多重大进展，它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具有重要意义，特别是它几乎重新配置了应用数学、数学物理和微分几何的许多领域。该计划在菲尔兹研究所打算专注于“当前的问题在椭圆和抛物线偏微分方程”，主要是在应用数学，数学物理和/或微分几何的动机领域。椭圆和抛物偏微分方程的理论出现在物理科学中的许多问题中，包括超导材料的结构，连续介质中的相变，新材料的新应用的微观结构，以及各种物理系统中图案形成的建模。在该领域有广泛的国际知名和活跃的研究人员，其中相当多的人将参加2003年秋季在菲尔兹研究所的专题学期。参加该计划的年轻美国研究人员将找到许多与其他学科，政府科学实验室以及工业领域的数学分析师和研究人员进行富有成效的合作的机会。组织委员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.