Explore a lecture on market design for priority-based assignment with distributional objectives, delivered by Atila Abdulkadiroglu from Duke University at the Simons Institute. Delve into an axiomatic approach for meeting distributional objectives while respecting priorities in resource allocation. Examine the characterization of choice rules using type-specific reserves and quotas for a single school's admission process. Learn about the regular reserves-and-quotas rule and its unique ability to minimize priority violations. Analyze the application of this rule in a multi-school setup and discover how the Deferred Acceptance mechanism can optimize priority-based assignments while satisfying distributional constraints.