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

Inside an insulating vacuum chamber in a tunnel about 100 meters below the surface of the Franco-Swiss plain near Geneva, packets of protons whirl around the 27-km circumference of the Large Hadron Collider (LHC) at a speed close to that of light, colliding every 25 nanoseconds at four beam crossings.

Robot Programming by Demonstration (PbD) examines methods by which a robot learns new skills through human guidance. Also referred to as learning by imitation, tutelage or apprenticeship learning, PbD takes inspiration from the way humans learn new skills by imitation, thereby developing methods by which new skills can be transmitted to a robot.

Solidication is one of the oldest processes for producing complex shapes for applications ranging from art to industry, and it remains as one of the most important commercial processes for many materials. Since the 1980's, numerous fundamental developments in the understanding of solidication processes and microstructure formation have come from both analytical theories and the application of computational techniques using commonly available powerful computers.

Linear operators in Hilbert space play a fundamental role in the formulation of quantum theory. This book offers a self-contained presentation of the most important tools and methods from Hilbert space theory, with particular focus on the spectral theory of self-adjoint operators.