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.
