8843-Noncommutative Geometry II (Fall 2004)

Jean Bellissard                                                                                                    Course taught with
Professor of Mathematics and Physics                                                               MATH 8843 BED CRN 88018
School of Mathematics, Skiles 132                                                                      
Phone: (404) 385-2179                                                                                           
Fax: (404) 894-4409                                                                                                     
e-mail: jeanbel@math.gatech.edu
 
 

Prerequisites:
Familiarity with functional analysis, Operator Theory and C*-algebras

Location and Schedule:
Skiles    Tuesday-Thursday


Course description 

This course will be continuation of the course taught in 2003 on the same subject.
However this course can be followed even if the 2003 course was not attended.
It will cover mainly the following topics

Basic properties of C*-algebras, traces, Dixmier Traces, differential algebra
Cycles, spectral triples
Hoshschild cohomology, cyclic cohomology
NC-Riemannian Spin Manifolds,  Rennie's Theorem , Noncommutative Spheres
Riemannian geometry on metric Cantor sets, on foliated spaces.

These lectures should interest students in Mathematics and
in Mathematical Physics.

References:  books, articles

A. Connes, Noncommutative Geometry, Acad. press, San Diego (1994)

  Joseph C. Varilly, Hector Figueroa, Jose M. Gracia-Bondia,
Elements of Noncommutative Geometry, Birkhauser Boston (2000).