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

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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.