Asymptotic geometry of sofic groups and manifolds

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The idea of approximation of infinite structures by means of finite or compact objects is prevalent in modern mathematics. It is the aim of this project to gain further insight into the structure of infinite groups and non-compact manifolds by means of sofic approximations. Sofic groups were introduced by Gromov some 20 years ago since then have played a fundamental role in various fields of pure and applied mathematics. We want to emphasise the fact that no discrete group is known to be non-sofic at the moment, and indeed studying consequences of existence of a sofic approximation can be considered as a way to find restrictions on the group implied by soficity.