This volume grew out from a one-semester research program at the Bernouilli Center (EPFL, Lausanne, Switzerland) from January to June 2007. The research articles and survey papers presented here highlight modern state of the art, current methods and open problems, and are of interest both to experts and graduate students in the fields of geometric combinatorics, theoretical computer science and geometric group theory (plus interactions between them). Indeed, the main research topics herein include the geometric, combinatorial and computational aspects of group theory. In particular, there is a focus on the study of large families of finite graphs with certain "expanding" properties and their embeddings into Hilbert and Banach spaces. Specifically, the authors investigate the structure of finitely generated groups giving rise to such graphs; in addition, new interactions with broad areas of theoretical computer science are considered.

The research articles and survey papers presented here are of interest both to experts and graduate students in the fields of geometric combinatorics, theoretical computer science and geometric group theory.

On Tensor Products of Group C* -Algebras and Related Topics - A Note on Laplace Operators on Groups - Bounded Cohomology and Cross Ratios - Metric Dichotomies - Asymptotic Problems in Algebraic Structures - Spectral Analysis of Metric Graphs and Related Spaces - Manifestations of Nonlinear Roundness in Analysis, Discrete Geomety and Topology - Fixed Point Properties in The Space of Marked Groups - A Pastiche on Embeddings into Simple Groups (following P.E. Schupp) - Some Notes on Property A - Index

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