Speaker: 沙熠，北京大学

Inviter: 苏阳

Title: Nielsen Realization Problem and Homotopy Coherent Action

Language: English

Time & Venue: 2026.09.21 14:30-15:00 南楼N820

Abstract: The Nielsen realization problem asks whether finite subgroups of mapping class groups can be realized as genuine group actions on manifolds. From a homotopy-theoretic perspective, we can consider the more flexible notion of a homotopy coherent action instead of a genuine action. It is natural to ask whether a subgroup could be realized by a homotopy coherent action when it fails to be realized as a genuine action. In this talk, I will first survey recent progress on these questions and then present our result on K3-type 4-manifolds. Our main tool is family Seiberg–Witten invariants. This is joint work with Yujie Lin.