中科院数学与系统科学研究院

数学研究所

中科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： 陈绿洲 博士（Purdue University）

题  目：Topological optimization and the stable commutator length

时  间：2023.03.03（星期五），09:00-10:00

地  点：Zoom会议：876 1256 8518 密码：20230303

摘  要：It is a relatively recent discovery in geometric topology that optimization problems of certain topological complexity are connected to important geometric and topological information. One example is the Gromov-Thurstonnorm, which is the minimal complexity of surfaces representing a given second homology class, and it is closely related to fibrations of 3-manifolds as surface bundles. This is an introductory talk on a relative version of the Gromov-Thurston norm called the stable commutator length (scl), which is the minimal complexity of surfaces bounding a given loop. I will explain its computation and sharp lower bounds in relation tolinear programming, as well as its close relation to various problems in topology and group theory.