MTH 831 (Fall 2019): Von Neumann Algebras

Instructor: Hanfeng Li

Office: 104 Mathematics Building.     Phone: 645-8762 

Office Hours: TBA

Lectures: TR 9:30am-10:50am

Room: 250 Math

Course Description

Von Neumann algebras are algebras of bounded linear operators on Hilbert spaces, closed under the adjoint operation and suitable topologies. They are noncommutative version of measure spaces. The study of von Neumann algebras is closely related to ergodic theory, L2-invariants, and mathematical physics. This course is an introduction to von Neumann algebras. We shall discuss von Neumann's double commutant theorem, Kaplansky's density theorem, comparison of projections, type classification, normal states, traces, and the hyperfinite II_1 factor.

Prerequisite

You should have taken MTH 731 Functional Analysis. Better to know the basics of C*-algebras, though not necessary.

Course Requirement

Each student is required to present a chosen topic in the class.

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