Math 607 SPRING 2016, List of lectures

  • On this page I will post content of all lectures with reference to the book. All handouts also will be posted here.
  • Monday, March 28: Overview of problems of representation theory. Equivariant vector bundles.
  • Wednesday, March 30: Equivariant line bundles on projective line and representations of sl(2). Differential operators on projective line.
  • Friday, April 1: Group SL(2) over finite field and its representations. Principal series.
  • Monday, April 4: Etale cohomology with compact support and Lefschetz number.
  • Wednesday, April 6: Drinfeld curve and Deligne-Lusztig induction. Quotients and invariants.
  • Friday, April 8: Deligne-Lusztig characters are cuspidal.
  • Monday, April 11: Scalar products of Deligne-Lusztig characters.
  • Wednesday, April 13: Some character values.
  • Friday, April 15: Reductive Lie algebras, Verma modules, multiplicities.
  • Monday, April 18: Review of algebraic groups.
  • Wednesday, April 20: Bruhat decomposition.
  • Friday, April 22: Cohomology of flag varieties.
  • Monday, April 25: Bruhat order.
  • Wednesday, April 27: Global sections of line bundles on flag varieties.
  • Friday, April 29: Borel-Weil-Bott theorem.
  • Monday, May 2: Sheaf of differential operators. Its associated graded and cotangent bundle. D-modules and quasi-coherence.
  • Wednesday, May 4: Global differential operators on flag varieties.
  • Friday, May 6: Flag varieties are D-affine.
  • Monday, May 9: Holonomic D-modules.
  • Wednesday, May 11: Regular singularities.
  • Friday, May 13: Riemann-Hilbert correspondence and perverse sheaves.
  • Monday, May 16: Simple perverse sheaves and Decomposition Theorem.
  • Wednesday, May 18: Hecke algebras and convolution.
  • Friday, May 20: Kazhdan-Lusztig polynomials and multiplicities in Verma modules.
  • Monday, May 23: Hecke algebra and induced modules.
  • Wednesday, May 25: Deligne-Lusztig theory for general groups.
  • Friday, May 27: Character sheaves.
  • Monday, May 30: Memorial Day.
  • Wednesday, June 1: Character sheaves and Springer representations.
  • Friday, June 3: Overview of geometric Satake isomorphism.
  • THE END.