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.

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