Equivariant cohomology, Localization
theorem and GKM theory
授课专家：桂弢（北京大学）
课程时间：2025年12月11,12,16,18,19日下午2:30-4:30
课程地点：数学学院东409（腾讯会议号：644-526-972）
课程信息：
Equivariant cohomology is a cohomology theory for a G-space, here G is a group. A moment graph is a labelled graph which encodes the "one-skeleton" of certain algebraic torus actions on the varieties. It is an amazing fact (usually refered as the localization theorem) that one can recover a lot of cohomological information about a variety from its moment graph. Under certain conditions, one can calculate the equivariant and ordinary cohomology of a variety using relatively simple commutative algebra, which is called GKM theory. This minicourse will cover principal bundles and classifying spaces, characteristic classes, definition of equivariant cohomology ("Borel construction"), localization theorem, moment graphs, and GKM theory, as well as an application on combinatorics: realizing the chromatic symmetric functions for the unit interval graphs via symmetric groups actions on the corresponding GKM graphs.
专家简介：
桂弢，北京大学北京国际数学研究中心博士后。2018年本科毕业于四川大学数学学院，2023年于中国科学院数学与系统科学研究院获得博士学位，师从席南华研究员。主要研究方向是李理论，表示论，组合代数几何与组合霍奇理论。
邀请人：范久瑜
