Explore the determinant maximization problem and its applications in machine learning, statistics, convex geometry, algorithmic game theory, and network design in this 28-minute lecture by Mohit Singh from Georgia Institute of Technology. Delve into the known results and techniques for solving this abstract problem, ranging from approximation algorithms to estimation methods. Focus on matroid intersection techniques and their connections to determinant maximization, while surveying various approaches including geometry of polynomials, sparse solutions, and convex programming. Gain insights into the Nash social welfare problem and its relation to mathematical programming in this Simons Institute talk on optimization and algorithm design.