2018/04/22 by Maria Gillespie, Gillespie, Maria · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #14N10 #14N15 #14N20 #Advanced Combinatorial Mathematics #Advanced Mathematical Theories and Applications #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #FOS: Mathematics #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.1804.08164
openalex publication_date 2018/04/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this tutorial, we provide an overview of many of the established combinatorial and algebraic tools of Schubert calculus, the modern area of enumerative geometry that encapsulates a wide variety of topics involving intersections of linear spaces. It is intended as a guide for readers with a combinatorial bent to understand and appreciate the geometric and topological aspects of Schubert calculus, and conversely for geometric-minded readers to gain familiarity with the relevant combinatorial tools in this area. We lead the reader through a tour of three variations on a theme: Grassmannians, flag varieties, and orthogonal Grassmannians. The orthogonal Grassmannian, unlike the ordinary Grassmannian and the flag variety, has not yet been addressed very often in textbooks, so this presentation may be helpful as an introduction to type B Schubert calculus. This work is adapted from the author's lecture notes for a graduate workshop during the Equivariant Combinatorics Workshop at the Center for Mathematics Research, Montreal, June 12-16, 2017.