SM-Special Year in Arithmetic Geometry at the CRM Barcelona

Arizona State University, Scottsdale AZ

Investigators

Abstract

This grant will support US-based speakers and other US-participants to attend the conference, Regulators III, to take place in July 2010 at the Centre de Recerca Matematica (CRM) in Barcelona, Spain. This is the culminating conference of a year-long program in arithmetic geometry at the CRM, and will attract many of the best researchers in the world. The funding will allow US-based researchers to learn of the latest developments in a field in which mathematicians from Europe and Asia have been playing an increasing role over the last 10 years. Recent developments in the subject include work on Beilinson?s conjecture on special values of L-functions of certain automorphic representations of a symplectic group in four variables, and the lack of surjectivity of certain regulators for generic surfaces of degree at least 5 in projective 3-space over p-adic fields. Regulators help to measure the size of objects in arithmetic and geometry, and they are a unifying theme in the subject. The definition and computation of regulators is a fundamental part of several parts of mathematics. One recent theme in the subject has been to transport techniques from arithmetic to geometric situations, and vice-versa. These methods have allowed us to demonstrate the existence of interesting elements of important arithmetic and geometric objects.