Groups and Operator Algebras Seminar

Speaker: Alessandro Vignati (Université de Paris Cité)

Title: Coarse equivalences, bijective coarse equivalences, and rigidity of uniform Roe algebras

Abstract: Uniform Roe algebras are C*-algebras capable of detecting the large scale geometry of metric spaces, important for their fruitful applications to coarse geometry, index theory, and mathematical physics. The rigidity problem asks whether two uniformly locally finite whose uniform Roe algebras are isomorphic must be bijectively coarse equivalent. Recently, a partial solution was given, and it was shown that in case two uniform Roe algebras are isomorphic the underlying spaces are coarsely equivalent. The main question of interest for us is then the following: when are coarse equivalences close to bijective coarse equivalences ? What can we say if the coarse equivalences of interest come from an isomorphism of uniform Roe algebras? In this talk, after having introduced all relevant concepts, we provide partial answers to the above questions.

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