Some Things We Do and Don’t Know About Knots

Dr. Jason DeBlois
Associate Professor
University of Pittsburgh

In this talk, “knot” will mean a circle embedded in three-dimensional space. These have been formally studied since the late 19th century. More recently, new computational and geometric tools have allowed us to make substantial progress on understanding the landscape of knots and their invariants, but they have also raised new questions. I will introduce the study of knots, sketch its history, and describe what is known (to me) about some of these questions relating to hyperbolic geometry.