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Session S10 - Categorification, Higher Representation Theory, and Homological Knot Invariants

Tuesday, July 20, 16:00 ~ 16:35 UTC-3

Braid varieties, weaves, and positroids.

José Simental Rodríguez

Max Planck Institute for Mathematics, Germany   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

To a positive braid we associate an affine algebraic variety that we call the braid variety. These varieties are closely related to and in some cases generalize well-known varieties that appear in Lie theory such as Richardson, positroid and open Bott-Samelson varieties. They are also closely related to the augmentation variety of a Legendrian link associated to the corresponding positive braid. I will define the braid varieties and explain some of their properties and the connections mentioned above as well as a diagrammatic calculus, the weaves from the title, to study them that is closely related to Soergel calculus but differs from it in key aspects. Time permitting, I will also explore the question on how to define these varieties for braid words which are not necessarily positive, and explain consequences for positroid varieties.

Joint work with Roger Casals (University of California, Davis), Eugene Gorsky (University of California, Davis) and Mikhail Gorsky (Université de Picardie Jules Verne).

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