Bhishan Jacelon: Traces and the nonunital circle

I will discuss the prospect of classifying, via traces, *-homomorphisms from \(C_0(0,1)\) to certain stably projectionless \(C^*\)-algebras with trivial \(K_1\). I will explain how to use such a result to study unitary orbits of unitaries in simple Z-stable algebras and also perhaps how one might prove tensorial self-absorption of the stably finite analogue of \(O_2\).