MTH 831 (Fall 2012): Group von Neumann algebras and L2-invariants
Instructor: Hanfeng Li
Office: 104 Mathematics Building. Phone:
Office Hours: W 3-4pm
Lectures: TR 2:00-3:20pm
Room: 150 Math
- Course Description
- We shall first discuss the basics of group von Neumann
algebras of countable discrete groups, including the canonical
trace, the Fuglede-Kadison determinant, and the Ore
localization. This part is also a brief introduction to operator
algebras. Then we shall discuss L2-invaraints, which
has origin in algebraic topology but uses the group von Neumann
algebra, including the L2-Betti number and the L2-torsion.
The second part is more homological algebraic.
Fundamentals of the Theory of Operator Algebras. Vol. I.
Elementary Theory by Kadison and
L2-Invariants: Theory and
Applications to Geometry and K-Theory by
- For the first part, you should know the basic functional
analysis. For the second part, you should have taken algebraic
topology course, and know fundamental group, universal covering
space, CW-complexes and cellular homology.
the course page