The goal of this one-week conference at the Fields Institute in Toronto is to induce and stimulate interactions and collaborations at the cutting edge of research on topology, functional analysis and noncommutative geometry, leading to new mathematical breakthroughs. Its aim is also to celebrate the 80th birthday of Paul F. Baum whose remarkable contributions to this area of mathematics can hardly be overestimated.

Key subjects are: the Baum-Connes conjecture, K-homology, large-scale geometry, representation theory, and spectral theory in noncommutative geometry. All of these develop index theory and thus are based on an interaction between analysis and topology-geometry. Some of these topics arose from classical problems in global analysis, index theory and topology and continue to have application there. Collectively they have become powerful and effective tools that bring geometric ideas to bear on the analysis of a wide range of nonstandard spaces (or noncommutative spaces) arising in mathematics and physics. It is the excitement of this interplay of methods and results that we intend to capture at this conference.

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