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

该奖项为NSF/CBMS区域会议提供支持：算子代数的K-理论及其在几何和拓扑学中的应用，将于2020年8月17日至21日在里约热内卢的波多黎各大学举行。 主讲人是德州农工大学鲍威尔数学系主任、大学特聘教授余国梁。 还将有关于特邀演讲者提供的补充主题的讲座。在过去的十年中，有令人兴奋的发展，在这一领域的研究与应用的几个领域的数学。主讲人和他的合作者在介绍和研究新概念方面做出了重大贡献。 会议讲座将突出最新的进展，确定有前途的新的研究方向，并帮助学生和早期职业数学家导航到这个令人兴奋但具有挑战性的研究领域的前沿。K-理论是数学中几个重要领域的统一主题，包括算子代数、几何、拓扑和数论。K-群是椭圆算子的主不变量和次不变量的容器。Guoliang Yu和他的合著者在引入和研究这些不变量以及开发新工具（如定量/受控K理论和局部化代数）方面做出了一些重大贡献。 Yu，Weinberger和Xie最近解决了关于更高rho不变量的可加性的长期开放问题。 这一结果对流形的非刚性有重要的应用。Yu-Guentner-Tessera发展了一个几何复杂性理论，证明了当几何复杂性有限时，关于流形刚性的稳定Borel猜想。 这CBMS系列讲座将被设计成一个友好的介绍这些最新的发展。 欲了解更多信息，请参阅会议网站-https://math.uprrp.edu/nfs_cbms_uprrp/This奖反映了NSF的法定使命，并已被认为值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估的支持。

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.