K-theory and Noncommutative Geometry

From August 31 to September 6, 2006 there will be a one-week Summer School and Research Conference on ``K-theory and Noncommutative Geometry'' in Valladolid, Spain. The field of algebraic K-theory is rapidly changing, thanks to the recent developments relating it to motivic cohomology, etale cohomology, C*-algebras, derived categories and cyclic homology. The field of noncommutative geometry is also rapidly changing with cyclic homology, C^*-algebras and derived category techniques playing a leading role. The two subjects have considerable overlap, as this list shows. Bringing together international experts in these related fields should result in the discovery of new connections between these branches of mathematics. This conference is part of an on-going attempt to link up several different areas of mathematics undergoing rapid development: algebra, especially its connections to algebraic geometry via K-theory; functional analysis, especially operators on objects of geometric interest; and geometry, especially those non-commuting aspects measured by cyclic homology. The research conference portion will expose them to the forefront developments in the subject, and the opportunity for researchers to interact will advance discovery and enhance partnerships.