|Date:||November 19, 2018|
|Place:||Lecture Hall, Research II|
Abstract: The unknotting number of a knot, the minimum number of crossing changes required to unknot it, is a simple and mysterious knot invariant. Several very simple questions about the unknotting number are open, and the answers to some of them use the advanced mathematics developed in the framework of TQFT-type invariants, such as Seiberg-Witten theory, knot Floer theory or Khovanov homology. We will survey some of the techniques, developments and open questions related to the unknotting number and will report on new lower bounds constructed from knot Floer homology and their applications.