This is the final talk in a 3-part series whose goal is to give background as well as a self contained proof of Chen's recent breakthrough on the KLS conjecture and slicing problem. After becoming familiar with the construction of stochastic localization and some of its basic properties, in this talk we'll complete the proof of Chen's result. If time allows, we will also discuss some extensions as well as the reduction between the KLS conjecture and the slicing problem. Video of first talk: https://www.ias.edu/video/chens-recent-breakthrough-kannan-lovasz-simonovits-conjecture-and-bourgains-slicing-problem Second talk: https://www.ias.edu/video/chens-recent-breakthrough-kannan-lovasz-simon…