Title: Many-body localization

Abstract: 
Many-body localization is a phenomenon in physics where a material 
fails to conduct any heat at all. One could say it is a regime of 
extreme validity of the KAM theorem  (folk wisdom has it that KAM theory 
is only applicable for systems with a few degrees of freedom, but 
in quantum mechanics there are good reasons to believe that it can 
apply to systems in the thermodynamic limit as well).
From the point of view of mathematics, localization is in fact much 
more accessible than basically any other phenomenon in condensed matter 
physics.
Our recent work (joint with F. Huveneers) on this has been mostly 
non-rigorous.
Depending on hints from the audience, I will either try to give a 
conceptual introduction or to discuss some of our work.