题目：The connecting homomorphism in Hermitian K-theory

报告人：谢恒 教授（中山大学）

摘要：Higher algebraic K-theory was introduced by Daniel Quillen in 1972, earning him a Fields Medal. In his work, Quillen constructs a localization sequence, which is a long exact sequence serving as a powerful computational tool in higher algebraic K-theory. However, the connecting morphism (aka. boundary map) in the localization sequence is too abstract, and Quillen remarks that his proof unfortunately does not shed much light on the nature of the boundary map. An intrinsic description of the connecting morphism remains a mystery to this day. Hermitian K-theory, which generalizes Quillen’s higher K-theory, was introduced by Bass and Karoubi in 1973. Hermitian K-theory also possesses a localization sequence and a connecting homomorphism. In this talk, I will provide a geometric description of the connecting homomorphism in Hermitian K-theory. As an application, I will demonstrate how to use this description of the connecting homomorphism to compute Hermitian K-theory of Grassmannians. This is joint work with Tao Huang.

报告人简介：谢恒教授于2015年获英国华威大学博士学位，主要从事代数K理论的理论研究，解决了1977年M.Knebusch提出的关于二次超曲面的Witt群的一些重要问题。研究成果发表在Advances in Mathematics、Proceedings of the London Mathematical Society、Documenta Mathematica等国际知名数学杂志。

时间：2024年4月9日（周二）下午14:00-15:30

地点：教二楼613教室

联系人：惠昌常、陈红星