A flag variety is a projective algebraic variety with a transitive action of a linear algebraic group. Flag varieties play an important role in the representation theory of algebraic groups as well as classical algebraic geometry. This course will begin with the basic structure of flag varieties and the Borel-Weil-Bott theorem describing the cohomology of line bundles on flag varieties. We will also consider various topics such as Springer’s construction of Weyl group representations, as well as connections to equivariant cohomology and degeneracy loci.
