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The categorified Burau representation

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HTLW01 - Winter school workshop

The goal of this talk will be to introduce a particularly important 2-representation of B_n – the categorified Burau representation – which appears prominantly in symplectic geometry, algebraic geometry, and in representation theory.  We will give several proofs of the faithfulness of this 2-representation, and explain how it allows us to study various structures on interest in braid theory (e.g. Garside structures, word-length metrics, left-invariant orders, etc.) using tools of linear and homological algebra.

This talk is part of the Isaac Newton Institute Seminar Series series.

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