The purpose of the International Stefan Banach Mathematical Centre school/conference on "Noncommutative Geometry and Quantum Groups" is twofold. The first aim is to provide an introduction and training in some of the mainstreams of geometry of noncommutative spaces and both algebraic and analytic theories of quantum groups by means of appropriate series of survey lectures. These survey lectures are designed to introduce the audience into the state-of-the-art of the following main research topics: Noncommutative Index Theory and Hopf Symmetry, Baum-Connes Conjecture Locally Compact Quantum Groups, Galois Type Extensions of Noncommutative Algebras.
The second goal is to enable an efficient communication of most recent results and enhance the mutual understanding among researchers working on different but strongly related aspects of quantum geometry. The hope is to encourage people to undertake research in these advanced and rapidly growing areas of mathematics, and to achieve the synergetic effect of cross-fertilization by combining complementary fields of expertise. Modern mathematical research frequently runs across the classical division of mathematics into particular subjects. The afore-stated combination of topics brings together algebra, analysis, differential geometry and K-theory techniques to address concrete mathematical problems, programmes and theories that were born in recent years. This bringing together of expertise ranging from pure algebra to functional analysis proves the particularly interdisciplinary character of this meeting. On the other hand, the well-focused programme of the school conference organizes this wide range of mathematical knowledge into coherent and manageable pieces.