Explore a 26-minute IEEE conference talk on improving approximations for graph crossing numbers. Delve into previous work on general and bounded-degree graphs, crossing numbers with rotation systems, and a new framework presented by Julia Chuzhoy, Sepideh Mahabadi, and Zihan Tan from Toyota Technological Institute at Chicago and the University of Chicago. Gain insights into the intuition behind Chuzhoy 11 and follow the plan for proving Main Theorem 1. Conclude with a comprehensive summary of the presented research and its implications for graph theory and computational geometry.