# Topics 1. Interacting Particle Systems & PDE ˆ 1. Granular Flow Models and McKean-Vlasov Equations. ˆ 2. Nonlinear Diffusion and Aggregation-Diffusion Equations. 2. Optimal Transportation: The metric side 1. Functional Analysis tools: weak convergence of measures. Prokhorov’s Theorem. Direct Method of Calculus of Variations. 2. Monge Problem. Kantorovich Duality. ˆ 3. Transport distances between measures: properties. The real line. Probabilistic Interpretation: couplings. 3. Mean Field Limit & Couplings ˆ 1. Continuity Equation: measures sliding down a convex valley.ˆ 2. Dobrushin approach: derivation of the Aggregation Equation. 3. Boltzmann Equation for Maxwellian molecules: Tanaka Theorem. 4. An Introduction to Gradient Flows 1. Dynamic Interpretation of optimal tranport. 2. McCann’s Displacement Convexity: Internal, Interaction and Confinement Energies. 3. Gradient Flows: Differential and metric viewpoints.