Title: Schubert calculus and flag manifolds
Prerequisites: basic mathematics maturity at the level of graduate algebra, or consent of
the instructor.
Course Description: Grassmannians and flag manifolds are among the most charismatic and ubiquitous algebraic varieties. They are important in many areas of mathematics, from representation theory to enumerative geometry to combinatorics. One reason for this is that they have very rich, interconnected, and well-understood geometric, combinatorial, and algebraic structures.
This course will treat many aspects of Grassmannians and flag manifolds, including their Schubert
decomposition, algebraic and combinatorial models for their cohomology rings, as well as symbolic
computation of Schubert problems from enumerative geometry.
Avg time dedicated per week (estimate): 3-5hrs