This volume offers an introduction, in the form of four
extensive lectures, to some recent developments in several active
topics at the interface between geometry, topology and quantum
field theory. The first lecture is by Christine Lescop on knot
invariants and configuration spaces, in which a universal
finite-type invariant for knots is constructed as a series of
integrals over configuration spaces. This is followed by the
contribution of Raimar Wulkenhaar on Euclidean quantum field theory
from a statistical point of view. The author also discusses
possible renormalization techniques on noncommutative spaces. The
third lecture is by Anamaria Font and Stefan Theisen on string
compactification with unbroken supersymmetry. The authors show that
this requirement leads to internal spaces of special holonomy and
describe Calabi-Yau manifolds in detail. The last lecture, by
Thierry Fack, is devoted to a K-theory proof of the Atiyah-Singer
index theorem and discusses some applications of K-theory to
noncommutative geometry. These lectures notes, which are aimed in
particular at graduate students in physics and mathematics, start
with introductory material before presenting more advanced results.
Each chapter is self-contained and can be read independently.
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