Asymptotic geometry of sofic groups and manifolds

用有限的或紧凑的物体逼近无限结构的思想在现代数学中很流行。本课题的目的是为了进一步深入了解无限群和非紧流形的结构。20多年前由Gromov提出的索菲亚群在纯数学和应用数学的各个领域发挥了重要作用。我们要强调的事实是，目前没有已知的离散群是非柔性的，而且确实，研究一个柔性近似存在的结果可以被认为是一种发现由柔性所隐含的群的限制的方法。

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.