Braid varieties are a family of varieties that arise naturally in representation theory. They generalize double Bruhat cells and positroids, and are useful for studying flag varieties, Schubert varieties, and Bott-Samelson varieties. In recent work with Casals, Gorsky, Gorsky, Shen and Simental, we show that a fairly general class of braid varieties admits a cluster structure. I'll explain some of the motivations for considering cluster structures coming from mirror symmetry and Legendrian knot theory.
Eric Zaslow
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