K-theory and Noncommutative Geometry

2006年8月31日至9月6日，西班牙巴拉多利德将举办为期一周的“K理论和非交换几何”暑期学校和研究会议。代数K-理论的领域正在迅速变化，这要归功于它与移动上同调、等上同调、C*-代数、派生范畴和循环同调有关的最新发展。非对易几何领域也在迅速地发生变化，循环同调、C^*-代数和导数范畴技巧占据主导地位。正如下面的清单所示，这两个主题有相当大的重叠。将这些相关领域的国际专家聚集在一起，应该会发现这些数学分支之间的新联系。这次会议是正在进行的尝试的一部分，目的是将正在快速发展的数学的几个不同领域联系起来：代数，特别是通过K-理论与代数几何的联系；泛函分析，特别是几何对象上的算子；以及几何，特别是那些通过循环同调测量的非对易方面。研究会议部分将使他们接触到该学科的前沿发展，研究人员互动的机会将促进发现并加强合作。

From August 31 to September 6, 2006 there will be a one-week SummerSchool and Research Conference on ``K-theory and NoncommutativeGeometry'' in Valladolid, Spain. The field of algebraic K-theory israpidly changing, thanks to the recent developments relating it tomotivic cohomology, etale cohomology, C*-algebras, derived categoriesand cyclic homology. The field of noncommutative geometry is alsorapidly changing with cyclic homology, C^*-algebras and derivedcategory techniques playing a leading role. The two subjects haveconsiderable overlap, as this list shows. Bringing togetherinternational experts in these related fields should result in thediscovery of new connections between these branches of mathematics.This conference is part of an on-going attempt to link up several differentareas of mathematics undergoing rapid development: algebra, especially itsconnections 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 forefrontdevelopments in the subject, and the opportunity for researchers tointeract will advance discovery and enhance partnerships.