Prof. Dr. Matthias Lesch
Mathematisches Institut

Seminar Sommersemester 2007

Seminar zur Globalen Analysis B:Cyclic cohomology and the noncommutative Chern character

Room and time have changed: Tuesday 10-12, Seminar room MPI

Noncommutative Geometry is an area of mathematics which has been dominated by the work of Alain Connes in the last 20-25 years. The basic idea is that instead of point sets (e.g. manifolds) one studies the coordinate ring of (smooth) functions. This point of view has been around in algebraic geometry for decades but it was Connes who showed that also manifolds and index theory can be understood from this perspective. Examples of "noncommutative spaces", where now the coordinate ring is a noncommutative algebra, are abundant and Noncommutative Geometry is an area of active current research. The purpose of this seminar is modest. We want to study some of the basic material of noncommutative geometry, like cyclic (co)homology, Fredholm modules, the noncommutative analogue of the classical Chern character and the Hochschild-Kostant-Rosenberg-Connes Theorem. For a first reading we will use an excellent survey by Higson. Since I also hope to attract international graduate students the seminar is going to be held in English.

When and Where: First Talk: Do, 05.04.07, 8:15 SR B. Regular Meetings: Tuesdays 10:15, Seminar room MPI See also weekly Program. If you are interested you should informally contact Matthias Lesch (lesch@math.uni-bonn.de) or Michael Bohn (mbohn@math.uni-bonn.de)

Schedule of talks:

  1. The Gelfand-Naimark Theorem and noncommutative topology (Matthias Lesch, 05.04.07)

  2. The trace and the Schatten ideals (Michael Bohn, 10.04.07)

  3. Fredholm modules and the index pairing (Bram Mesland, 17.04.07)

  4. The character of a finitely summable Fredholm module (Bram Mesland, 24.04.07)

  5. Hochschild (co)homology (Carolina Neira, 03.05.07, Hausdorff-Raum, Beringstr. 3) Notice the date and the room!

  6. Cyclic (co)homology I (Dapeng Zhang, 22.05.07)

  7. Cyclic (co)homology II (Dapeng Zhang, 29.05.07)

  8. The Hochschild-Kostant-Rosenberg-Connes Theorem (NN)

  9. The noncommutative Chern character I (NN)

  10. The noncommutative Chern character II (NN)

Detailed Program.