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Noncommutative Geometry is one of the most deep and vital research
subjects of present-day Mathematics. Its development, mainly due to
Alain Connes, is providing an increasing number of applications and
deeper insights for instance in Foliations, K-Theory, Index Theory,
Number Theory but also in Quantum Physics of elementary particles.
The purpose of the Summer School in Martina Franca was to offer a
fresh invitation to the subject and closely related topics; the
contributions in this volume include the four main lectures, cover
advanced developments and are delivered by prominent specialists.
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