" C*-approximation theory has provided the foundation for many of the most important
conceptual breakthroughs and applications of operator algebras. This book systematically …

Large scale geometry is the study of geometric objects viewed from a great distance. The
idea of large scale geometry can be traced back to Mostow's work on rigidity and the work of …

Index theory studies the solutions to differential equations on geometric spaces, their
relation to the underlying geometry and topology, and applications to physics. If the space of …

We prove that for any free ergodic probability measure preserving action Γ→(X, μ) of a non-
elementary hyperbolic group, or a lattice in a rank one simple Lie group, the associated …

We provide an expository account of Guoliang Yu's property A. The piece starts from the
basic definitions, and goes on to discuss closure properties of the class of property A spaces …

We prove a Kurosh-type theorem for free-product type II 1 factors. In particular, if M= LF 2⊗
ℛ, then the free-product type II 1 factors M∗⋯∗ M are all prime and pairwise nonisomorphic …

The author obtains some classification result for the mapping class groups of compact
orientable surfaces in terms of measure equivalence. In particular, the mapping class groups …

Uniform embeddability of relatively hyperbolic groups Page 1 J. reine angew. Math. 612 (2007),
1—15 DOI 10.1515/CRELLE.2007.081 Journal für die reine und angewandte Mathematik …

We study graph products of groups from the viewpoint of measured group theory. We first
establish a full measure equivalence classification of graph products of countably infinite …

We provide a general criterion to deduce maximal amenability of von Neumann subalgebras
L Λ⊂ L Γ arising from amenable subgroups Λ of discrete countable groups Γ. The criterion is …