Explore a groundbreaking lecture in the Breakthroughs series by Yuansi Chen from Duke University, delving into the significant progress made on the Kannan-Lovász-Simonovits (KLS) Conjecture. Learn about the almost constant lower bound of the isoperimetric coefficient, its implications for Monte Carlo sampling theory, and the innovative proof techniques employed. Discover the key components of the proof, including the localization lemma, variation lemma, and algorithmic inequality. Gain insights into the advantages of this new approach and its potential impact on related fields of mathematics and computer science.