Explore particle methods for optimization over measures in this lecture by Lenaic Chizat, part of the Data Science: Probabilistic and Optimization Methods discussion meeting at the International Centre for Theoretical Sciences. Dive into advanced mathematical concepts and their applications in data science, focusing on the intersection of optimization techniques and measure theory. Gain insights into cutting-edge research and methodologies that drive the current data science revolution. Learn how these particle methods contribute to solving complex optimization problems in various fields, including machine learning and statistical physics. Understand the theoretical foundations and practical implications of this approach, which combines elements from probability theory, optimization, and functional analysis.