Topological Methods in Contextuality - A Unified Framework for Simplicial Distributions

Explore a 25-minute lecture from CLEA at the Free University of Brussels (VUB) that delves into the advanced mathematical framework of simplicial distributions for studying contextuality. Learn how measurements and outcomes are represented through spaces rather than discrete label sets, with a focus on simplicial sets as fundamental objects in modern homotopy theory. Discover the application of topological tools in examining state-independent contextuality and understand how the sheaf-theoretic framework, introduced by Abramsky and Brandenburger, utilizes Cech cohomology to study contextuality scenarios. Master the unified theoretical approach that combines and extends both the topological and sheaf-theoretic methods through simplicial distributions.