Speaker：Zhaojun Chen (California Institute of Technology)

Time：2025-8-15 10:00

Location：Conference Room C503 at Administration Building at Haiyun Campus

Abstract:

In this talk, we explore knot Floer homology (HFK), a powerful combinatorial and homological invariant for knots in the 3-sphere. Developed by Ozsváth and Szabó, HFK associates a bigraded vector space to a knot, refining fundamental invariants like the Alexander polynomial and the knot genus. We outline the foundational ideas behind HFK, including its construction via Heegaard diagrams or grid diagrams. We also examine key properties of HFK, such as its role in detecting the Seifert genus and fiberedness of knots. Furthermore, we discuss its relationship to the three-genus, slice genus, and the broader landscape of knot concordance. Finally, we touch upon the computational aspects and significance of HFK in modern low-dimensional topology.