Abstracts
for the Seminar

Fall 2024

**Speaker: **Lucas Gagnon, York University

**Title: **The quasisymmetric flag variety and equivariant forest polynomials

**Time:** 2:30 PM, Monday, November 11, 2024

**Place:** Malott 206

**Abstract:** Schubert calculus transforms the intersection theory of the flag variety $GL_n/B$ into a multiplication problem involving combinatorial polynomials, while double Schubert calculus extends this to a torus-equivariant setting. Two essential components underlie these approaches: (1) a surjective homomorphism from the infinite polynomial ring $R[x_1, x_2,\dots]$ to the (torus-equivariant) cohomology ring of $GL_n/B$, and (2) the existence of Schubert polynomials, a basis of $R[x_1, x_2,\dots]$ that interacts naturally with the surjection from (1). In this talk, I will introduce a subvariety of $GL_n/B$ and a basis of $R[x_1, x_2, \dots]$ that exhibit remarkably close analogues of (1) and (2). I will show how these new objects can be analyzed using tools from algebraic combinatorics such as noncrossing partitions and quasisymmetric polynomials, and then I will speculate about how this can deepen our understanding of Schubert calculus. This is ongoing work with Nantel Bergeron, Philippe Nadeau, Hunter Spink, and Vasu Tewari.

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