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.
Monday, April 4: Etale cohomology with compact support and Lefschetz number.
Wednesday, April 6: Drinfeld curve and Deligne-Lusztig induction. Quotients
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.