Beijing Institute of Mathematical Sciences and Applications

Intersection theory is a central tool connecting algebraic geometry, topology, representation theory, and mathematical physics. Enumerative geometry provides a natural setting in which abstract geometric concepts lead to explicit and meaningful computations. This course introduces the fundamental ideas of intersection theory and their applications to enumerative geometry. It develops the geometric and algebraic tools needed to understand how geometric objects intersect and how intersection numbers can be used to solve counting problems in algebraic geometry. The course emphasizes both conceptual foundations and concrete computations, with examples drawn from projective spaces, Grassmannians, and related homogeneous varieties.