Crossing Numbers of Whitehead Doubles

Explore the intricacies of knot theory in this 57-minute lecture by Christine Ruey Shan Lee from the University of South Alabama. Delve into the challenging problem of determining minimal crossing numbers of knots, with a focus on Whitehead doubles. Learn how the colored Jones polynomial can be applied to study crossing numbers, and discover the connection between polynomial degree asymptotics and crossing numbers. Examine an infinitely family of satellite knots and their minimum crossing numbers. The talk covers general results, satellites, an infinite family, Jones polynomials, attitude, resolution, and nonadequate diagrams. This lecture, presented at the University of Miami, offers valuable insights into advanced knot theory concepts and techniques.