IMS Inner Seminar 1: Knot operations and Floer homology of immersed curves

Seminarj| Institute of Mathematical Sciences

Time: Thursday, September 19th, 2024 , 14:30-15:30

Speaker: Wenzhao Chen, ShanghaiTech

Abstract: Knots can be modified through cut-and-paste operations like satellite operations and tangle replacements, giving rise to various measures of complexity. For instance, the unknotting number is one such measure. In this talk, I will present how immersed-curve techniques, which provide a geometric approach to knot homology theories, can be applied to compute and define numerical invariants that serve as bounds for these measures of knot complexity, helping to study of several open questions. This talk is based on joint work in progress with Jonathan Hanselman and Liam Watson.