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

主要研究人员将于2008年6月2日至6日在美国西南部沃斯堡的德克萨斯基督教大学组织CBMS （Conference Board of The Mathematical Sciences）关于拓扑、C*-代数和弦对偶性的会议，邀请马里兰大学的Jonathan Rosenberg教授担任主要发言人。会议的目的是向不同的观众，特别是年轻的研究人员，展示一个令人兴奋的研究领域的概述，该领域结合了拓扑学、算子代数和数学物理的思想。强烈鼓励来自不同背景的参与者进行互动。讲座的中心焦点将是尝试将弦理论中的t二象性建立在坚实的数学基础上。t对偶性的概念表明，当第一个时空中的圆（比如半径为R）被它们的“对偶圆”（半径为1/R）所取代时，有时两个不同的时空在物理上是不可区分的。我们将研究如何用拓扑或C*-代数来解释这种对偶性（至少部分解释）。Rosenberg教授的10场讲座将主要集中于以下主题：(1)弦理论的基本结构和t -对偶思想；(2)k理论及其与物理学的关系；(3)连续迹C*-代数、扭曲k -理论、C*-交叉积及其k理论；(4)t -对偶和t -对偶的交叉积拓扑；(5)用拓扑方法研究高维t -对偶；(6)用C*-代数方法研究高维t -对偶。最后，在时间允许的情况下，我们将讨论从其他角度处理字符串对偶性的一些高级主题和开放问题。

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.