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

Perverse Sheaves and Decomposition theorem I

by Omar Antolín Camarena and Chris Brav | University of Toronto
Time: 09:30 — 11:00  (Tuesday, Mar. 09, 2010)
Location: BA6180, Bahen Center, 40 St George St
Abstract:
Perverse Sheaves (Omar): This week we'll conclude our discussion of IC-sheaves by defining constructible complexes of sheaves are and describing Goresky and MacPherson's axioms characterizng IC-sheaves among constructible complexes. Relaxing these axioms in the middle perversity case gives the definition of perverse sheaves. We'll discuss some basic properties of the category of perverse sheaves.

Decomposition theorem I (Chris): We discuss further properties of the category of perverse sheaves, state the decomposition theorem for proper maps between algebraic varieties, and consider some consequences of the decomposition theorem. Next time we shall compute some examples and (maybe) outline a proof.

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)