# Basic notions in cotangent Schubert calculus

*Lecture given at the Introductory Workshop: Combinatorial Algebraic Geometry, ICERM, Brown University, February 1-5, 2021*

**Abstract: **

*A key notion of Schubert Calculus is the cohomology ring of a homogeneous space, together with a distinguished basis: the collection of Schubert classes. There is a one-parameter deformation of the notion “Schubert class’’, called Chern-Schwartz-MacPherson (CSM-) class (a.k.a. characteristic cycle class, or cohomological stable envelope). In this lecture/workshop we will define the CSM class, and illustrate many of its properties through examples.*

**Slides:**

- Introduction and H^*_T(Gr)
- Grassmannian
- Schubert cells
- Schubert Classes Gr(2,4)
- CSM Classes
- R Matrix property of CSM classes
- MacPherson Property of CSM classes
- Why “Cotangent” Schubert calculus
- Recursion
- Formulas
- K Theoretic Version: motivic Chern class, convex polygons
- Enumerative geometry

Problems for the problem session.