Postcards from oases in the desert phenomenology of SUSY with intermediate scales

The presence of new matter elds charged under the Standard Model gauge group at intermediate scales below the Grand Unication scale modies the renormalization group evolution of the gauge couplings. This can in turn signicantly change the running of the Minimal Supersymmetric Standard Model parameters, in particular the gaugino and the scalar masses. In the absence of new large Yukawa couplings we can parameterise all the intermediate scale models in terms of only two parameters controlling the size of the unied gauge coupling. As a consequence of the modied running, the low energy spectrum can be strongly aected with interesting phenomenological consequences. In particular, we show that scalar over gaugino mass ratios tend to increase and the regions of the parameter space with neutralino Dark Matter compatible with cosmological observations get drastically modied. Moreover, we discuss some observables that can be used to test the intermediate scale physics at the LHC in a wide class of models.