Topics course in Fall 2022

Title: Schubert calculus and flag manifolds

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.  On 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.

The prerequisites are basic mathematics maturity at the level of gradate algebra, or consent of
the instructor.  The grading will be based on a few homework sets, and then presentations at the
end of the semester of group projects.

Reference books:
 Young tableaux, by William Fulton
    I will also be considering other texts, as there is no book which covers the all the material
    I intend to touch on in this class.