Lorentz Center Conference on KK-Theory, Gauge Theory, and Topological Phases

奖项：DMS 1664597，主要研究者：Steven Rosenberg该奖项为美国参与提供部分支持- 2017年2月27日至3月10日，在荷兰莱顿举行的一所国际学校的数学家和与物质拓扑相有关的数学研讨会。 凝聚态物理学中当前感兴趣的显着现象被描述为材料系统的新相或属性，受复杂数学结构指定的规则的约束。 这次国际会议将包括一个为期一周的学校，让初级参与者在该地区的数学和物理背景和第二周的高级研究会谈研讨会。 本次会议旨在激发不同背景的研究人员之间的合作，并加强K理论和KK理论（卡斯帕罗夫双变K理论）的数学对该主题的贡献。很少有研究人员具有研讨会所有三个主题（规范理论，卡斯帕罗夫KK理论和物质的拓扑相）的背景，因此这次跨学科会议旨在使所有这些社区受益。 KK理论和非对易几何的最新发展，如卡斯帕罗夫乘积的构造性方法，似乎与当前的凝聚态物理学有关。预计讨论的相关数学主题包括KK理论中的对应关系、边界问题、规范理论中的新方法、指数理论的应用。

Award: DMS 1664597, Principal Investigator: Steven RosenbergThis award provides partial support for participation by U.S.-based mathematicians at an international school and workshop in mathematics related to topological phases of matter to be held in Leiden, the Netherlands, on February 27 - March 10, 2017. Remarkable phenomena of current interest in condensed matter physics have been described as new phases or properties of material systems, subject to rules specified by sophisticated mathematical structures. This international meeting will include a one-week school to give junior participants background in the mathematics and physics of the area and a second-week workshop of advanced research talks. The conference aims to spark collaborations between researchers of varied backgrounds and to enhance the contributions of the mathematics of K- and KK-theory (Kasparov's bivariant K-theory) to the subject.Few researchers have background in all three topics of the workshop (gauge theory, Kasparov KK-theory, and topological phases of matter), so this interdisciplinary conference aims to be of benefit to all of these communities. Recent developments in KK-theory and noncommutative geometry, such as a constructive approach to the Kasparov product, seem relevant to current condensed matter physics. Related mathematical topics on which discussions are expected include correspondences in KK-theory, boundary issues, new methods in gauge theory, applications to index theory.