CBMS Conference: K-theory of Operator Algebras and Its Applications to Geometry and Topology

该奖项为将于2020年8月17-21日在波多黎各大学里约皮德拉斯举行的NSF/CBMS区域会议：K-算子代数理论及其在几何和拓扑中的应用提供支持。主讲嘉宾为德州农工大学鲍威尔数学系讲座教授、大学特聘教授余国良。此外，还将由受邀演讲者就补充主题发表演讲。在过去的十年里，这一研究领域取得了令人振奋的发展，应用到了数学的几个领域。主讲人和他的合作者为介绍和研究新概念作出了重大贡献。会议讲座将突出最近的进展，确定有前途的新研究方向，并帮助不同的学生群体和早期职业数学家导航到这一令人兴奋但具有挑战性的研究领域的前沿。K-理论是几个重要数学领域的统一主题，包括算子代数、几何、拓扑学和数论。K-群是椭圆算子的主不变量和次不变量的容器。余国良和他的合著者在引入和研究这些不变量以及发展新的工具，如定量/控制K-理论和局部化代数方面做出了一些重要贡献。Yu，Weinberger和Xie最近解决了关于高Rho不变量的可加性的长期悬而未决的问题。这一结果对流形的非刚性有重要的应用。Yu-Guentner-Tessera发展了几何复杂性理论，证明了当几何复杂性为有限时关于流形刚性的稳定Borel猜想。这个CBMS系列讲座旨在友好地介绍这些最新的发展。有关更多信息，请参阅会议网站-https://math.uprrp.edu/nfs_cbms_uprrp/This奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

This award provides support for the NSF/CBMS regional conference: K-theory of operator algebras and its applications to geometry and topology, to be held during August 17-21, 2020 at the University of Puerto Rico at Rio Piedras. The principal speaker is Guoliang Yu, Powell Chair in Mathematics and University Distinguished professor at Texas A&M University. There will also be lectures on complementary topics delivered by invited speakers. In the last decade, there have been exciting developments in this field of research with applications to several areas of mathematics. The principle speaker and his collaborators have made significant contributions to introducing and studying new concepts. The conference lectures will highlight the recent advances, identify promising new research directions, and help a diverse group of students and early career mathematicians navigate to the frontier of this exciting yet challenging research field. K-theory is a unifying theme in several important areas of mathematics including operator algebras, geometry, topology, and number theory. K-groups are receptacles for both primary and secondary invariants of elliptic operators. Guoliang Yu and his coauthors have made several significant contributions to introducing and studying these invariants and developing new tools such as quantitative/controlled K-theory and localization algebra. Yu, Weinberger, and Xie recently solved the long standing open problem regarding additivity of higher rho invariants. This result has important applications to non-rigidity of manifolds. Yu-Guentner-Tessera developed a theory of geometric complexity to prove the stable Borel conjecture on rigidity of manifolds when the geometric complexity is finite. This CBMS lecture series will be designed to be a friendly introduction to these recent developments. For more information, see the conference website- https://math.uprrp.edu/nfs_cbms_uprrp/This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.