Topology of Algebraic Varieties

This is a learning seminar on the topology of algebraic varieties.  We will cover Lefschetz theory, intersection homology, perverse sheaves, and applications to representation theory.

http://wiki.math.toronto.edu/TorontoMathWiki/index.php/Topology_of_Algebraic_Varieties_Learning_Seminar

Kazhdan-Lusztig polynomials

by Brad Hannigan-Daley | University of Toronto
Time: 09:30 — 11:00  (Tuesday, Apr. 13, 2010)
Location: BA6180, Bahen Center, 40 St George St
Abstract:
Given a Coxeter group W, its Hecke algebra is a one-parameter deformation of the group algebra W which comes with two canonical bases. The transition matrix between these bases is described by the Kazhdan-Lusztig polynomials. These polynomials are defined combinatorially, but in the case that W is the Weyl group of a semisimple linear algebraic group $G$, they can be interpreted geometrically as generating functions for intersection Betti numbers of Schubert varieties in the flag variety $G/B$. We will discuss this correspondence, focusing on the case $G=SL_n$.

Dates in this series

· Tuesday, Jan. 19, 2010: Cohomology of families of smooth projective varieties (Stephen Morgan)
· Tuesday, Jan. 26, 2010: Intersection Homology Theory (Mikhail Mazin)
· Tuesday, Feb. 02, 2010: Intersection homology (continued) (Mikhail Mazin)
· Tuesday, Feb. 09, 2010: Sheaf Cohomology, Derived and Triangulated Categories (Arthur Huang)
· Tuesday, Feb. 23, 2010: Sheaf Cohomology, Derived and Triangulated Categories (Continued) and IC-Sheaves (Arthur Huang/Omar Antolín Camarena)
· Tuesday, Mar. 02, 2010: IC-sheaves and Perverse Sheaves (Omar Antolín Camarena)
· Tuesday, Mar. 09, 2010: Perverse Sheaves and Decomposition theorem I (Omar Antolín Camarena and Chris Brav)
· Tuesday, Mar. 16, 2010: Applications of the decomposition theorem (Chris Brav)
· Tuesday, Mar. 23, 2010: Semismall maps and Springer theory (Sergey Arkhipov)
· Tuesday, Mar. 30, 2010: Semismall maps and Springer theory - Part II (Sergey Arkhipov)
· Tuesday, Apr. 13, 2010: Kazhdan-Lusztig polynomials (Brad Hannigan-Daley)
· Thursday, Apr. 15, 2010: The Geometric Satake Correspondence (Bruce Fontaine)
· Tuesday, Apr. 20, 2010: The Riemann-Hilbert Correspondence (Daniel Rowe)