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

The Riemann-Hilbert Correspondence

by Daniel Rowe | University of Toronto
Time: 09:30 — 11:00  (Tuesday, Apr. 20, 2010)
Location: BA6180, Bahen Center, 40 St George St
Abstract:
Classically, the Riemann-Hilbert problem roughly asks: given a space X, and any monodromy (representation of π1, local system on X), does there exist a differential equation having this prescribed monodromy on its solutions? The answer is affirmative, and a modern formulation of this phenomenon is via an equivalence of the derived category of regular holonomic D-modules on X and the derived category of constructable sheaves on X. The most important feature of this is an equivalence between the full abelian subcategory of regular holonomic D-modules and the nonstandard heart of perverse sheaves on X. I plan to overview the requisite notions and explain this correspondence and some applications.

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)