The investigators will establish a Center for Arithmetical Algebraic Geometry at the University of Arizona, in collaboration with the Universities of New Mexico, Southern California, and Texas. The center will further the research of the principal investigators; provide a forum for studying, extending, and disseminating the latest results in arithmetical algebraic geometry and related fields; and enhance the education and professional development of graduate students and recent PhDs in mathematics. Arithmetical algebraic geometry is a field of fundamental research which has its roots in classical problems of arithmetic and geometry, both highly abstract (such as expressing integers as sums of squares) and completely concrete (such as laying out fields for agriculture). On the other hand it has experienced tremendous advances in the twentieth century and is still vitally active today, as evidenced by such heroic advances as Faltings' resolution of the Mordell conjecture and Wiles' proof of Fermat's Last Theorem. Moreover, it has retained its relevance to contemporary life through its connections with robot control, computer vision, RSA data encryption, efficient audio and video compression algorithms, and other aspects of information technology.
