Explore particle methods for optimization over measures in this comprehensive lecture by Lénaïc Chizat, part of the Data Science: Probabilistic and Optimization Methods discussion meeting. Delve into advanced mathematical concepts and techniques used in data science, focusing on the analytic and algorithmic aspects of processing large-scale data. Gain insights into the intersection of pure mathematics and practical applications in the rapidly evolving field of data science. Learn about the latest developments in optimization, linear algebra, probability, and statistics as they relate to solving complex data-driven problems. Understand how these methods contribute to the ongoing revolution in data processing and analysis across various scientific disciplines.