Schubert calculus

Schubert calculus is a branch of mathematics that studies how to count and understand the ways geometric objects, like lines, planes, and higher-dimensional shapes, intersect within algebraic varieties such as Grassmannians. It uses combinatorial and algebraic techniques to solve problems about the number of solutions or arrangements of these intersections, often represented through special polynomials called Schubert polynomials. This field combines geometry and algebra to answer questions about the structure and enumeration of intersections, with applications in areas like enumerative geometry and representation theory.