**Speaker:** Bruno de Mendonça Braga, Puc-Rio

**Title:** Embeddings of von Neumann algebras into uniform Roe algebras

*Place: Pontificia Universidad Católica, Facultad de Matemáticas, Campus San Joaquin, Sala 1*

**Abstract:**

Given a uniformly locally finite metric space X, its uniform Roe algebra, denoted by C^{∗}_{u}(X), is a C^{∗}-algebra of bounded operators on the Hilbert space ℓ^{2}(X) which captures the large scale geometry of X. This algebra was introduced by John Roe in 1988 and it has since become a topic of interest to researchers in many different fields such as operator algebras, geometric group theory, and mathematical physics. As for the latter, uniform Roe algebras have recently started to be used as a framework in mathematical physics to study the classification of topological phases. In this talk, we will discuss some recent developments about the structure of C^{∗}_{u}(X). More precisely, we discuss which von Neumann algebras can be found inside C^{∗}_{u}(X).