Explore the SDP relaxation technique for the Max-Cut problem in this graduate-level lecture from Carnegie Mellon University's "CS Theory Toolkit" course. Learn how to transform an exact quadratic program into a linear program with infinite constraints, and discover how this relaxation leads to a semidefinite program solvable by the Ellipsoid Algorithm. Delve into advanced topics in theoretical computer science, drawing from resources like "Geometric Algorithms and Combinatorial Optimization" and "Laplacian eigenvalues and the maximum cut problem." Taught by Professor Ryan O'Donnell, this 33-minute lecture covers key concepts including linear programming, the Ellipsoid Algorithm, and semidefinite programming, providing essential knowledge for research in theoretical computer science.