A Reduction Approach to the Positivity Conjecture of Band Bases on Surfaces with Boundary
数学专题报告
报告题目(Title)：A Reduction Approach to the Positivity Conjecture of Band Bases on Surfaces with Boundary
报告人(Speaker)：孙林（北京师范大学）
地点(Place)：后主楼1220
时间(Time)：2026年6月3日（周三）15:00-15:55
邀请人(Inviter)：肖杰、覃帆、周宇
报告摘要
A recent advancement in this area is Queffelec's proof of the positivity of the band basis on closed surfaces without marked points. Based on this work, in this talk, we prove the positivity conjecture for unpunctured surfaces with boundary. By introducing a geometric reduction via topological surgery—capping boundary components and attaching 1-handles—we transform arcs into loops on a closed surface. Moreover, we establish a bijection to transfer the known positivity results from the closed case back to the original surface. This is a joint work with Jizhe Huang, Fan Qin, and Yabo Zhou.
