All aforementioned works have advanced the state of the art in the field. Two theoretical results we have obtained are likely to have a strong impact on the field in due time.
The first result, concerns our discovery classical mechanical systems which realize topological phenomena which was previously thought to be inherently quantum. Although these are currently only theoretical models, there is ongoing work by us and collaborators in ETH aimed at realizing such model in the lab. Since these are classical models, this should be far easier than realizing their quantum counterparts. Nonetheless their exotic behavior, which include stable critical behavior on surface, has never been witnessed before. New an exotic physical phenomena often find their way to technological applications.
The second result, concerns the relation we exposed between geometric responses--- motion of charge/energy following bends and twists in the geometry, and computation complexity. Roughly speaking, we showed that the way some phases of matter react when coupled to gravity implies that their equilibrium properties cannot be efficiently calculated using a classical computer. Connecting these two very different aspects of a physical system - its computation complexity and its response to gravity, may very well be of fundamental importance. As this is fundamental research it is premature to talk about specific technological implications.
From a much broader point of view this projects deals with an ubiquitous phenomena--- the fact that many simple interacting components, in our case spins or electrons, often lead to strange and diverse behaviors. Our world is becoming more advance and complex exactly from those reasons: Many brokers interacting in the Stock market, many artificial neurons interacting in artificial intelligence architectures, and many different processes interacting to create our ecological systems. Condensed matter physics, while not dealing directly with such real world scenario, has provided important conceptual tools to tackle such complex problems and will most likely do so also in the future.
