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.

More information on this seminar series can be found at the following link:

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

Details

Sheaf Cohomology, Derived and Triangulated Categories (Continued) and IC-Sheaves

by Arthur Huang/Omar Antolín Camarena | University of Toronto
Time: 09:30  (Tuesday, Feb. 23, 2010)
Location: BA6180, Bahen Center, 40 St George St
Abstract:
IC-sheaves: As Deligne suggested, for any fixed perversity, the construction of the chain complex Goresky and MacPherson use to define intersection homology can be repeated on every open set, thus defining a complex of sheaves called the IC-sheaf for that perversity. The original intersection cohomology groups are recovered as the hypercohomology of the space with coefficients in the IC-sheaf. There is an alternate construction of IC-sheaves applying a sequence of "extensions" and truncations to the constant sheaf. This description has the advantage that the constant sheaf can be replaced with a locally constant sheaf, allowing us to define intersection cohomology with coefficients in a local system.

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)