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Learn about cluster algebras in this 45-minute conference talk from the Amplituhedra, Cluster Algebras, and Positive Geometry Conference. Explore the fundamental concepts of these commutative rings, originally introduced by Fomin and Zelevinsky in 2002 for studying total positivity and canonical basis in Lie Theory. Discover the basic properties of cluster algebras, including positivity and Laurent phenomenon, while examining their connections to various areas of mathematics and physics. Delve into cluster structures derived from coordinate rings of Grassmannians and understand the combinatorics of plabic graphs through expert instruction from University of Kentucky's Khrystyna Serhiyenko.
