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Braid varieties and algebraic weaves

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Jose Simental Rodriguez
Don, 12/08/2021 - 15:00 - 16:00
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Meeting ID: 931 7291 0947
For password please contact Christian Kaiser (

To a positive braid in n strands we associate an algebraic variety that we call the braid variety. This is an affine, smooth variety defined by explicit polynomial equations and it is closely related to classical Lie-theoretic varieties such as Richardson varieties and open Bott-Samelson varieties, as well as the augmentation variety of the Legendrian link given by the rainbow closure of the braid. I will explain these connections and move on to the algebraic weaves, which are a graphical calculus for producing stratifications of the braid varieties by affine spaces and tori. Time permitting, I will explain how to go about defining these varieties when the braid is not necessarily positive. This is joint work with Roger Casals, Eugene Gorsky and Mikhail Gorsky.

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