Abstract: We will discuss a new program of studying ambient
obstruction solitons using a geometric flow for a general tensor
q. We begin by establishing a number of results for solitons to the
q-flow. Examining both the compact and non-compact cases, we ascribe
properties to q allowing us to prove that certain solitons are
q-flat. Specifically, we will consider a number of regularity
conditions on X that enable the use maximum principle type
arguments. Finally, we apply these results to the ambient obstruction
flow, the Bach flow (n ≥ 5), and the Cotton flow demonstrating the
utility of this approach.