Ivo Dell'Ambrogio: Equivariant tensor triangulated categories of C∗-algebras

Abstract: Among triangulated categories arising in Nature, we find several families whose objects are C∗-algebras (so, noncommutative topological spaces) possibly equipped with a group action, or fibred over a space, etc. Generally speaking, these are not as well understood as the probably more familiar triangulated categories arising in algebra and topology: they have no good natural choices of models, enhancements, or sets of generators, and typically only have countable coproducts at best. Still, they are central objects of interest, and there are some recent hopeful developments. In this talk I will attempt an up-to-date overview of these creatures, paying particular attention to equivariant KK-theory and how it compares to similar tt-categories in algebra, geometry and topology.