中国科学院数学与系统科学研究院

数学研究所

中国科学院华罗庚数学重点实验室

华罗庚青年数学论坛

综合报告

报告人： 孙巍峰 博士 （斯坦福大学）

题  目：Some potential applications of gauge theory in knot theory

时  间：2023.11.03（星期五），09:00-10:00

地  点：Zoom会议：897 1288 6628  密码：1103

摘  要：It is well-known that certain PDEs in gauge theory (on a low dimensional manifold) can give us useful topological and geometrical information of the background manifold. It is also known that studying solutions of these PDEs with a knot singularity maygive us useful information about the knot lying in the manifold. Some famous and successful examples of the PDEs include the Yang-Mills equations and the Seiberg-Witten equations etc..

In this talk, I'll introduce some recent work on studying the Bogomolny equations and the Kapustin-Witten equations with certain types of knot singularity. These PDEs, which are also originated from gauge theory in physics, also have the potential to studyknot invariants in the future.