Hermitian K-theory of Grassmannians

讲座题目Title：Hermitian K-theory of Grassmannians

讲座时间 Datetime: 2024.6.12  15:00-17:15

地点 Venue: 海琴2号楼A412-1

报告人 Speaker: 谢恒 教授

单位 Affiliation: 中山大学数学学院

主持人Host：张磊 副教授

报告摘要 Abstract:

Hermitian K-theory, a cohomology theory, has found interesting applications in recent works. Through a series of works by Asok, Fasel, and Srinivas, the obstruction class for splitting algebraic vector bundles is shown to reside in Hermitian K-theory under certain conditions. Moreover, Hermitian K-theory aids in understanding an unsolved problem on the composition of quadratic forms posed by Hurwitz in 1898. However, not many computations have been done in Hermitian K-theory. Pushforward is a powerful computational tool in cohomology theory. Recently, we developed pushforward in Hermitian K-theory via Grothendieck's residue complex. Additionally, we have proven the base change, projection, and excess intersection formulas. These tools allow us to compute the Hermitian K-theory of   Grassmannians, leading to a special class of Young diagrams that we call buffalo-check Young diagrams. This is joint work with Tao Huang.

报告人简介：

谢恒老师是中山大学数学学院的副教授。主要研究领域是K-理论，二次型，代数闭链。在著名数学杂志Proceedings of the London Mathematical Society, Advances in Mathematics, Documenta Mathematica等发表论文多篇。