MTH 831 (Fall 2012): Group von Neumann algebras and L2-invariants

Instructor: Hanfeng Li

Office: 104 Mathematics Building.     Phone: 645-8762 

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.
Recommended Reading
           About operator algebras:   Fundamentals of the Theory of Operator Algebras. Vol. I. Elementary Theory    by Kadison and Ringrose,
           About L2-invariants:          L2-Invariants: Theory and Applications to Geometry and K-Theory     by Luck.
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.

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