250148 VO Symmetric functions in geometry (2018S)

This course is about computations of various geometric invariants with a particular stress on the use of symmetric functions. The course assumes knowledge of basic linear algebra (matrices) and algebra (groups, polynomials). All the background from algebraic geometry and algebraic topology will be explained during the course.

In particular we are going to cover the following topics: symmetric functions, representations of symmetric and general linear groups, Schur-Weyl duality, geometry of Grassmannians and flag manifolds, vector bundles, K-theory, characteristic classes, Hirzebruch-Riemann-Roch theorem, Borel-Weil-Bott theorem.

Lecture notes will be gradually appearing here:
https://www.dropbox.com/s/87dollku59qy6rq/symfunc.pdf?dl=0