This volume contains the proceedings of an NSF-CBMS Conference held at
Texas Christian University in Fort Worth, Texas, May 18–22,
2009. The papers, written especially for this volume by well-known
mathematicians and mathematical physicists, are an outgrowth of the
talks presented at the conference. Topics examined are highly
interdisciplinary and include, among many other things, recent results
on D-brane charges in $K$-homology and twisted
$K$-homology, Yang-Mills gauge theory and connections with
non-commutative geometry, Landau-Ginzburg models,
$C^*$-algebraic non-commutative geometry and ties to quantum
physics and topology, the rational homotopy type of the group of
unitary elements in an Azumaya algebra, and functoriality properties
in the theory of $C^*$-crossed products and fixed point
algebras for proper actions. An introduction, written by Jonathan
Rosenberg, provides an instructive overview describing common themes
and how the various papers in the volume are interrelated and fit
together. The rich diversity of papers appearing in the volume
demonstrates the current interplay between superstring theory,
geometry/topology, and non-commutative geometry. The book will be of
interest to graduate students, mathematicians, mathematical
physicists, and researchers working in these areas.

Readership

Graduate students and research mathematicians interested in the
relations between mathematical physics and various areas of pure
mathematics.