Explore continuous algorithms for sampling and optimization in high dimensions in this 33-minute lecture by Santosh Vempala from Georgia Tech, presented at the Simons Institute 10th Anniversary Symposium. Delve into topics such as the Cutting Plane method, Rounding and Integration, Interior-Point Method 2.0, and Riemannian Hamiltonian Monte Carlo. Learn about the challenges of optimization, the complexity of solving linear systems, and discover a template for continuous algorithms. Gain insights into finding the right space and path for effective problem-solving in high-dimensional contexts.