Boundary maps on group C*-algebras

Boundary actions of groups (in the sense of Furstenberg) were brought to the attention of operator algebraists in 2014 through the theorem of Kalantar and Kennedy, which asserts that the reduced C*-algebra of a discrete group is simple if and only if the group admits a topologically free boundary action. This talk will advertise the study of an important class of maps defined on G-C*-algebras, called boundary maps, by using them to efficiently prove the Kalantar-Kennedy theorem. We will end with a discussion of more recent results.