报告题目：The positive fundamental group of Sp(2n)

报 告 人：王俭 副教授 (南开大学)

报告时间：2026年1月12日 15：30-16：30

报告地点：数学楼研讨室五

校内联系人：赵雪峰 [email protected]

报告摘要：We study the homotopy theory of positive loops in the real symplectic group $\mathrm{Sp}(2n)$. We prove that two positive loops are homotopic if and only if they are homotopic through positive loops, thereby providing a positive answer to a question by Lalonde and McDuff in 1997. As geometric applications, we remove the four–dimensional restrictions in results of McDuff and Chance on Hamiltonian loops with fixed global maxima: their uniruledness criteria extend verbatim to arbitrary dimension. In particular, if a nontrivial element of $\pi_1(\mathrm{Ham}(M,\omega))$ admits a Hofer length–minimizing representative, then $(M,\omega)$ is uniruled. This is a joint work with Qinglong Zhou.

报告人简介：王俭，南开大学数学科学学院副教授，主要研究方向为曲面动力系统、辛动力系统与辛几何。博士毕业于清华大学&巴黎第十三大学，曾在南开大学陈省身数学研究所、德国马普所-莱比锡数学所（MPI-MIS）、巴西国家纯数学与应用数学研究所（IMPA）做博士后，独立地或与他人合作在 GAFA, Advances in Math., TAMS, IMRN, AHP-C等国际知名数学期刊发表论文多篇。