The Average Genus of a 2-Bridge Knot Grows Linearly with Respect to Crossing Number

The Average Genus of a 2-Bridge Knot Grows Linearly with Respect to Crossing Number

Explore a mathematical lecture on the linear growth of the average genus of 2-bridge knots in relation to crossing number. Delve into the experimental data from Dunfield et al, and examine the proof for 2-bridge knots using Chebyshev billiard table diagrams developed by Koseleff and Pecker. Investigate the speaker's previous work with Krishnan and Even-Zohar on a random model, and learn about the improved results demonstrating a lower bound for the average genus among weighted 2-bridge knots. Gain insights into this joint work by Moshe Cohen and Adam Lowrance, presented at the University of Miami, which builds upon and enhances existing research in knot theory.