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This talk from the Workshop on "Recent Perspectives on Non-crossing Partitions through Algebra, Combinatorics, and Probability" at the Erwin Schrödinger International Institute explores the relationship between non-crossing partitions and webs. Discover how webs provide a diagrammatic calculus for spaces of SL(r)-tensor invariants, with a focus on recent joint work introducing hourglass plabic graphs as a new avatar of webs to create the first rotation invariant SL(4)-web bases. Learn about a construction that generates an hourglass plabic graph from a non-crossing partition and its Kreweras complement, which recovers Chris Fraser's rotation-invariant web basis for Plücker degree two representations of arbitrary SL(r). The 33-minute presentation delivers advanced mathematical concepts at the intersection of algebra, combinatorics, and representation theory.
