At the same time, dealing with mutlidimensional spaces is getting increasingly important, particularly in computer science. In this course we will study essentially the only nontrivial insight that mathematicians presently have into the nature of multidimensionality, known as the phenomenon of concentration of measure on high-dimensional structures, and its applications. The course will be mostly dedicated to very concrete objects, such as spheres and hypercubes, and abstract generalisations will play a secondary role.
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