US - Morocco Workshop on Geometric Analysis of Several Complex Variables and Related Topics, May 2010; Marrakech, Morocco

该奖项将于2010年5月在摩洛哥马拉喀什举办为期一周的研讨会，讨论多复变量、偏微分方程及相关主题领域的最新进展。该研讨会将在马拉喀什的K 'enitra的Ibn Tofail大学举行，由来自佛罗里达国际大学的Abdelhamid Meziani博士及其国际合作者联合组织，包括Youssef Barkatou（普瓦捷大学），Shiferaw Berhanu（坦普尔大学），Abdelhamid Meziani（佛罗里达国际大学），Rafik Meziani（Ibn Tofail大学）和Nordine Mir（鲁昂大学）。一些组织和机构为研讨会提供资金支持，包括美国国家科学基金会，国际数学联盟，法国国家研究机构（ANR）以及普瓦捷和鲁昂大学。与会者将包括来自美国，法国，巴西和马格里布（摩洛哥，突尼斯，阿尔及利亚）的主要研究人员，以及来自美国和马格里布地区的大量早期职业研究人员和研究生。 与会者之间的思想交流旨在促进这些领域的进一步合作和进展，并将为初级与会者提供指导。函数和映射的切向柯西-黎曼方程组提供了偏微分方程超定系统的重要例子。一个经典的和著名的例子，系统的这种由于汉斯路易发挥了核心作用，发展的可解性理论更一般类的偏微分方程。同样的例子也激发了并将继续激发对CR函数和映射的规律性的积极研究。 许多关于线性和非线性偏微分方程的超定系统的问题和结果都受到了CR情形的启发。 因此，CR几何和分析专家的参与对研讨会特别重要。PDE、CR几何和全纯叶理之间的相互作用已经很好地建立起来。一个例子说明了这一点是最近的兴趣，复杂的分析和PDE专家在显示不存在的真实的列维平坦超曲面在复杂的射影空间。 这个问题来自于全纯叶理和动力学理论，最初是由Cerveau在90年代初提出的。 近年来，对叶理的几何学、分类和正常形态的研究迅速增长。研讨会的参与者所使用的技术与此专业知识可以被带入分析问题处理解析hypoellipticity或与障碍的可解性的某些系统的偏微分方程。更广泛的影响：研讨会将提供一个极好的机会，为美国和国际研究生和早期的职业科学家学习和交流思想与世界各地的领导人在这些领域的数学。八名美国研究生和最近的博士学位。来自美国的一些人被邀请参加研讨会。 许多青年数学家（20多名来自马格里布）将参加。该研讨会包括两个迷你课程，专为研究生和早期职业科学家，将重点放在CR几何和分析的最新发展。迷你课程的讲义将发布在研讨会的网站上，会议记录将发表在适当的期刊上。该奖项由NSF国际科学与工程办公室支持。

This award is providing support for a week long workshop in Marrakech, Morocco, in May 2010, to discuss the recent progress in the fields of Several Complex Variables, Partial Differential Equations, and related topics. The workshop will take place at the University Ibn Tofail of K´enitra in Marrakech and is being jointly organized by the Dr. Abdelhamid Meziani from Florida International University and his international collaborators, including Youssef Barkatou (University of Poitier), Shiferaw Berhanu (Temple University), Abdelhamid Meziani (Florida International University), Rafik Meziani (Ibn Tofail University), and Nordine Mir (University of Rouen). A number of organizations and institutions are providing funding support for the workshop including the US National Science Foundation, the International Mathematical Union, the French National Research Agency (ANR), and the Universities of Poitiers and Rouen. The participants will include leading researchers from the US, France, Brazil, and the Maghreb (Morocco, Tunisia, Algeria), as well as a large number of early career researchers and graduate students from the US and the Maghreb region. The exchange of ideas among the participants is intended to stimulate further collaboration and progress in these fields and will provide guidance to the junior participants.The systems of tangential Cauchy-Riemann equations for functions and mappings offer important examples of overdetermined systems of partial differential equations. A classical and famous example of a system of this kind due to Hans Lewy played a central role in the development of the solvability theory for more general classes of PDEs. The same example also inspired and continues to inspire a vigorous investigation of the regularity of CR functions and mappings. Many questions and results on overdetermined systems of linear and nonlinear PDEs are inspired by what is known in the CR case. The participation of experts on CR geometry and analysis is therefore of particular importance for the workshop. The interplay between aspects of PDE, CR geometry, and Holomorphic Foliations are well established. One example illustrating this is given by the recent interest of complex analysis and PDE experts in showing the non-existence of real Levi-flat hypersurfaces in complex projective spaces. The question comes from holomorphic foliations and dynamics theory and was originally raised by Cerveau in the beginning of the 90's. Studies of the geometry of foliations and of the classification and normal forms have seen rapid growth in recent years. The techniques being used by workshop participants with this expertise can be brought into analyzing problems dealing with analytic hypoellipticity or with the obstruction to solvability of certain systems of PDE.Broader impacts: The workshop will provide an excellent opportunity for US and international graduate students and early career scientists to learn and exchange ideas with worldwide leaders in these areas of mathematics. Eight US graduate students and recent Ph.D.'s from the U.S. have been invited to the workshop. A large number of young mathematicians (over 20 from the Maghreb) will be participating. The workshop includes two mini courses designed for the graduate students and early career scientists that will focus on recent developments in CR Geometry and Analysis. The lecture notes of the mini courses will be posted on the website of the workshop and the proceedings will be published in an appropriate journal.This award is being supported by NSF Office of International Science and Engineering.