Local-to-Global Theorems on High Dimensional Expanders

Explore high dimensional expansion theory in this Institute for Advanced Study colloquium lecture that extends traditional graph expansion concepts to higher dimensional mathematical structures. Delve into the fascinating emergence of global properties from local characteristics in high dimensional expanders, with particular focus on cosystolic expansion and link expansion definitions. Learn how these theoretical advances have contributed to breakthroughs in error-correcting codes and Probabilistically Checkable Proofs (PCPs). Discover the mathematical principles behind these complex structures and their practical applications in computational theory, guided by expert insights into this evolving field of study.