Algebra-Geometry-Combinatorics Seminar
Nov 14, 2024 3:00 - 3:50 pm
Altgeld Hall 143
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- Algebra-Geometry-Combinatorics Seminar
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- Mathematics Seminar Series: Algebra, Geometry, and Combinatorics
Speaker: David Wallach (UIUC)
Title: Words and Schubert Calculus
Abstract: Giving a combinatorial explanation for the positivity of Schubert structure constants is a longstanding open problem. In this talk, which is based on joint work with Andy Hardt, we introduce an algebra on “chromatic words” which is homomorphic to the ring of back-stable quasisymmetric functions. By analyzing the preimage under this homomorphism of the product of two back-stable Schubert polynomials, we give a word-theoretic re-expression of the Schubert problem.