Prof. Allen Knutson's Math 7310, Fall 2010

Monday/Wednesday 11:40-12:55 in Malott 206

Course description here.

Course notes here, through the first week or two. Its table of contents is

  • Spaltenstein's theorem and Hotta's construction
  • Equivariant cohomology and divided differences
  • Review of the Bruhat decomposition
  • The Steinberg variety
  • Geometric construction of U_q(n_+) for simply-laced Lie algebras
  • Grojnowski-Nakajima quiver varieties
  • Ginzburg's geometric construction of representations of SL(n)
  • The affine Grassmannian
  • The geometric Satake correspondence
  • Intersection cohomology and perverse sheaves
  • Mirkovi\´c-Vilonen cycles
  • Some other resources:
  • Lectures on Hall algebras chapters 1-3, by Olivier Schiffmann
  • Lectures on canonical and crystal bases of Hall algebras chapters 1-3, by Olivier Schiffmann
  • Keep up with the class blog.