Hyperbolic geometry is one of the fundamental geometry in dimension 3 by Thurston's Geometrization theorem. Part I of the talk will introduce fundamental properties in hyperbolic geometry and its interplay with the fundamnental groups and dynamics of the manifolds. Heegaard Floer homology is a package of 3-manifold invariants defined from a very different perspective, and it is a very effeicent tool to study 3-, 4-manifolds. Part II of the talk will concentrate on nice applications of this new tool in low dimensinal topology. Last part of the talk will give open questions regarding to hyperbolic geometry and Heegaard Floer homology.

个人简介：刘贝贝，俄亥俄州立大学助理教授。2013年本科毕业于正规外围买球十大平台，2019年博士毕业于加利福尼亚大学戴维斯分校，曾在马普数学所、乔治亚理工学院和麻省理工学院从事研究工作。研究方向为几何与拓扑，在 Geometry & Topology, Quantum Topology, Transactions of AMS, IMRN 等期刊发表论文10余篇。