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Explore advanced mathematical concepts in this lecture from Cornell University's Allen Knutson examining the unification of hybrid pipe dreams and generic pipe dreams in relation to Schubert polynomials. Delve into the connection between two pipe dream formulae, focusing on hybrid pipe dreams developed with Udell and generic pipe dreams created with Zinn-Justin. Learn about the computation of equivariant cohomology classes of lower-upper varieties and discover how they recover Schubert polynomials as leading terms. Examine the development of 2n hybrid generic pipe dream formulae and their associated Yang-Baxter equations in this collaborative work with Paul Zinn-Justin, presented at the Workshop on Combinatorics of Enumerative Geometry.
