Classification of short-range entangled quantum states and pumping processes

I will introduce the topic of classification of short-range entangled quantum states. Physically speaking, these states are ground states of gapped Hamiltonians without any intrinsic topological order (ie. no anyonic excitations, for example), but one can define them in a neat abstract way that avoids such elaborate concepts.

I will try to sketch some open problems, and some results. In particular on the classification of pumping processes of such states, which can be viewed as a generalization of Thouless pumps.