# Surveys in Noncommutative Geometry

Share this page *Edited by *
*Nigel Higson; John Roe*

A co-publication of the AMS and Clay Mathematics Institute

In June 2000, the Clay Mathematics Institute organized
an Instructional Symposium on Noncommutative Geometry in conjunction with the
AMS-IMS-SIAM Joint Summer Research Conference. These events were held at Mount
Holyoke College in Massachusetts from June 18 to 29, 2000. The Instructional
Symposium consisted of several series of expository lectures which were
intended to introduce key topics in noncommutative geometry to mathematicians
unfamiliar with the subject. Those expository lectures have been edited and are
reproduced in this volume.

The lectures of Rosenberg and Weinberger discuss various applications of
noncommutative geometry to problems in “ordinary” geometry and
topology. The lectures of Lagarias and Tretkoff discuss the Riemann hypothesis
and the possible application of the methods of noncommutative geometry in
number theory. Higson gives an account of the “residue index
theorem” of Connes and Moscovici.

Noncommutative geometry is to an unusual extent the creation of a single
mathematician, Alain Connes. The present volume gives an extended
introduction to several aspects of Connes' work in this fascinating
area.

Titles in this series are co-published with the Clay Mathematics Institute (Cambridge, MA).

#### Readership

Graduate students and research mathematicians interested in noncommutative geometry.