Explore a comprehensive lecture on convergent semi-Lagrangian methods for the Monge-Ampère equation on unstructured grids. Delve into the challenges of numerically solving fully nonlinear second-order partial differential equations, focusing on Monge-Ampère type equations. Discover a new approach that establishes an equivalent Bellman formulation and designs monotone numerical methods for general triangular grids. Learn about the application of Howard's algorithm for robust computation of numerical approximations on fine meshes. Examine the rigorous convergence analysis, comparison principle for the Bellman operator, and treatment of boundary conditions. Gain insights into the connection between Monge-Ampère and Hamilton-Jacobi-Bellman equations, and understand their applications in optimal transport and inverse reflector problems. Follow the presentation's structure, covering motivation, viscosity solutions, equivalence, comparison principles, convergence, boundary conditions, and numerical experiments. Read more