报告题目：Recent progess on the Busemann conjecture and Busemann spaces

报告人：谷世杰教授东北大学

报告时间：2026.11.05 10:00-11:00

报告地点：腾讯会议会议ID 762128459

参会密码：123456

校内联系人：王骁 [email protected]

报告摘要：The Busemann conjecture asserts that every finite-dimensional Busemann G-space is a topological manifold, linking the local behavior of geodesics to the topology of the underlying space. I will discuss recent joint work with Tadashi Fujioka on this conjecture and on Busemann spaces of nonpositive curvature. A highlight is the resolution of the last open case of Gromov's 1981 question: every topological 4-manifold equipped with a complete metric of global Busemann nonpositive curvature is homeomorphic to R^4. We also establish the Busemann conjecture when sufficiently small metric balls are convex, and prove the disjoint disks property for every finite-dimensional Busemann G-space of dimension at least five. By the Edwards-Quinn recognition theorem, the latter result reduces the conjecture in these dimensions to the existence of cell-like manifold resolutions. The talk will emphasize the interaction between synthetic geometry and geometric topology.

报告人简介：

谷世杰，2018年获美国威斯康星大学密尔沃基分校博士学位。2019-2022年曾任美国中央康涅狄格州立大学助理教授。2022年7月至今任东北大学海外百人青年特聘教授，博士生导师。主要从事几何拓扑学的研究,涉及流形的拓扑与度量几何学。