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Explore the mathematical concept of plabic tangles in this 52-minute conference talk that introduces a novel framework connecting planar bipartite graphs to cluster algebra structures. Learn about plabic tangles as planar bipartite graphs drawn inside input disks with associated output disks positioned in the graph's faces, and discover how these structures generate promotion maps - rational mappings from input Grassmannians to products of output Grassmannians. Examine the conditions under which these promotion maps maintain compatibility with cluster algebra structures on Grassmannians, with particular attention to the BCFW promotion example used to prove the cluster adjacency conjecture for the amplituhedron. Gain insights into cutting-edge research at the intersection of combinatorics, algebraic geometry, and mathematical physics through detailed examples and theoretical foundations developed through collaborative work with Chaim Even-Zohar, Matteo Parisi, Melissa Sherman-Bennett, and Ran Tessler.
