This project will support US-based researchers attending an international program on the arithmetic geometry of function fields of positive characteristic at the "Centre de Recerca Matematica" (CRM) in Barcelona, Spain, during the spring of 2010. The program will include graduate courses, two international workshops, and an advanced course on recent developments. It is expected that researchers from around the world will attend and that notes from some of the courses and workshops will be published.
Arithmetic geometry is the study of questions originating in number theory using the methods and tools of algebraic geometry. The field has seen recent spectacular advances (such as the proof of Fermat's Last Theorem) and applications to contemporary technologies such as reliable communications and information security. A great deal of insight has been gained from the analogies and interactions between arithmetical structures (such as the rational numbers) and more geometric structures (such as polynomial functions on the line). This workshop will continue the exploration of these analogies and interactions.
