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This lecture titled "Combinatorics in Quantum K-theory Schubert Calculus" by Cristian Lenart from the University at Albany explores applications of the quantum alcove model in the torus equivariant quantum K-theory of flag manifolds G/B. Discover how this uniform combinatorial model, based on Weyl group combinatorics, enables the expression of a Chevalley-type multiplication formula in quantum K-theory. Learn about the model's various ramifications, including solutions to longstanding conjectures such as the Buch-Mihalcea conjecture, which serves as a replacement for the "divisor axiom" in quantum K-theory of G/B. The lecture explains how this conjecture demonstrates that a K-theory Gromov-Witten invariant of Chevalley type equals a classical (degree 0) invariant. The presentation includes collaborative work with Satoshi Naito, Daisuke Sagaki, and other researchers, and is part of the Special Year Seminar I series at the Institute for Advanced Study.
