NSF/CBMS Regional Conference in the Mathematical Sciences: Topology, C*- algebras, and String Duality, June 2008

Texas Christian University, Fort Worth TX

Investigators

Abstract

The Prinicpal Investigators will organize a CBMS (Conference Board of the Mathematical Sciences) conference on Topology, C*-algebras, and String Duality from June 2 to June 6, 2008, to be held in the southwest region of the United States at Texas Christian University in Fort Worth, Texas, featuring Professor Jonathan Rosenberg of the University of Maryland as the principal speaker. The purpose of the meeting will be to present to a diverse audience, especially to young researchers, an overview of an exciting area of research combining ideas from topology, operator algebras, and mathematical physics. Interaction of participants from all backgrounds will be strongly encouraged. The central focus of the lectures will be on attempts to put T-duality in string theory on a firm mathematical foundation. The idea of T-duality suggests that sometimes two different space-times are physically indistinguishable when circles in the first space-time (say of radius R) are replaced by their "dual circles" (of radius 1/R). We will examine how such a duality can be explained (at least in part) in terms of topology or C*-algebras. Professor Rosenberg's 10 lectures will focus primarily on the following topics: (1) The basic structure of string theories and the idea of T-duality, (2) K-theory and its relevance to physics, (3) Continuous-trace C*-algebras, twisted K-theory, C*-crossed products, and their K-theory, (4) The topology of T-duality and T-duality via crossed products, (5) Higher-dimensional T-duality via topological methods, and (6) Higher-dimensional T-duality via C*-algebraic methods. Finally, some advanced topics and open problems dealing with string duality from other perspectives will be discussed as time permits.