The five lectures include: (1) Introduction to synthetic Ricci bounds; (2) Variable Ricci bounds: equivalence of Eulerian and Lagrangian approach to curvature-dimension conditions with variable curvature bounds; (3) Distributional valued Ricci bounds; (4) Time change, localization, and convexification; (5) Gradient estimates for Neumann heat flow on non-convex and convex domains.
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