Geometry of flag varieties

Instructor: Joel Kamnitzer,
Lectures: MWF 1:00 - 2:00 Fields library
Office: 6110 Bahen 416-978-5163
Office Hours: Wednesday 10:00 - 12:00

Grading scheme:

  • Three assignments.

  • Syllabus:
    Schubert cells and varieties
    Borel-Weil Theorem
    Springer Theory
    Affine Grassmannians

    There is no single reference for what I am covering. Here are some suggested readings. We won't be covering all of what is in these books. Rather each book contains some sections relevant what we are doing.
  • Fulton, Young tableaux
  • Fulton and Harris, Representation Theory
  • Ginzburg and Chriss, Representation Theory and Complex Geometry
  • Bjorner and Brenti, Combinatorics of Coxeter Groups
  • Dimca, Sheaves in Topology
  • Arabia, Faisceaux pervers et Correspondence de Springer
  • Zhu, Introduction to affine Grassmannians and the geometric Satake equivalence
  • Me, Representations of GL_n, geometric Satake and categorification

  • Homework:
    Assignment 1 (pdf, tex) due Friday October 14.
    Assignment 2 (pdf, tex) due Friday November 11.

    Here are my handwritten notes. Warning: these notes are very sketchy and may not correspond exactly to what I said during lecture.
    September 12-30
    October 10-14
    October 17-19
    October 21-26
    October 28-November 2
    November 4-21