"Universal Superfuid Transition and Transport Properties 
of Two-Dimensional Dirty Bosons"
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  The interplay of disorder and interactions has been at the center of intense
theoretical and experimental activity the past decades. It sustains rich phase
diagrams, relevant to a wide range of condensed-matter systems. Recent
evelopments with ultracold atoms spark a renewed interest and open new
challenging issues. For instance, in interacting systems on the continuum, the
intervening phases are largely debated and still in a conjectural stage.  In
this talk I will discuss the phase diagram of disordered and interacting
ultracold atoms in two dimensions, that we have obtained thanks to accurate,
large-scale Quantum Monte Carlo simulations.[I] I will show that the superfuid
transition is strongly protected against disorder, up to the zero-temperature
Bose-glass transition. Most of its critical properties can be understood in terms
of an universal BKT description with a simple scaling of the critical
temperature versus the disorder strength.  I will then address the strongly
disordered regime at finite temperature where the possible existence of a 
(many-body) localized phase constitutes a challenging open question. Thanks to a
taylored methodological improvement, we have gained direct access to the
conducting properties. I will show that the finite-temperature insulating phase
merging at large disorder strength is well described by a thermally activated
behavior of the Arrhenius type.