Title: Flag varieties and Schubert calculus Lecturer: Arun Ram, University of Melbourne Abstract: Schubert calculus is the study of the structure of flag varieties. An example of a flag variety is the set of k-dimensional subspaces of a vector space (when k=1, this gives us projective space). The structure of flag varieties is intimately connected to the combinatorics of symmetric functions, and Schubert calculus is the mechanics for doing computations in flag varieties with polynomials. This course will be a survey of how we play this game.