seminar FisMat

FisMat Seminar, Septiembre 7, 2022, 15:30

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

Given a uniformly locally finite metric space X, its uniform Roe algebra, denoted by Cu(X), is a C-algebra of bounded operators on the Hilbert space ℓ2(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 Cu(X). More precisely, we discuss which von Neumann algebras can be found inside Cu(X).