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On Schubert polynomials

Karola Mészáros, Cornell University
Wednesday, May 12, 2021 - 3:30pm to 5:00pm
via Zoom

Note: This talk begins with a pre-seminar (aimed at graduate students) at 3:30–4:00. The main talk starts at 4:10.

Join Zoom Meeting:
Meeting ID: 915 4733 5974

Schur polynomials are specializations of the integer point transforms of Gelfand-Tsetlin polytopes. Schubert polynomials are specializations of integer point transforms of Minkowski sums of Gelfand-Tsetlin polytopes for column-convex permutations. We can also view Schubert polynomials as weighted integer point transforms of their Newton polytopes. We prove that the Newton polytopes of Schubert polynomials are generalized permutahedra and establish various properties of the Schubert coefficients. Inspired by our study of Schubert coefficients as well as our polytopal view, we establish nonnegative linear combinations of Schubert polynomials with monomial coefficients. This talk is based on joint works with Alex Fink, June Huh, Ricky Liu, Jacob Matherne, Avery St. Dizier and Arthur Tanjaya.