Lepton Flavour Violation in charged leptons within SUSY-seesaw

In this paper we review our main results for Lepton Flavour Violating (LFV) semileptonic tau decays and muon-electron conversion in nuclei within the context of two Constrained SUSY-Seesaw Models, the CMSSM and the NUHM. The relevant spectrum is that of the Minimal Supersymmetric Standard Model extended by three right handed neutrinos, $\nu_{R_i}$ and their corresponding SUSY partners, ${\tilde \nu}_{R_i}$, ($i=1,2,3$). We use the seesaw mechanism for neutrino mass generation and choose a parameterisation of this mechanism that allows us to incorporate the neutrino data in our analysis of LFV processes. In addition to the full one-loop results for the rates of these processes, we will also review the set of simple formulas, valid at large $\tan \beta$, which are very useful to compare with present experimental bounds. The sensitivity to SUSY and Higgs sectors in these processes will also be discussed. This is a very short summary of the works in Refs. \cite{Arganda:2008jj} and \cite{Arganda:2007jw} to which we refer the reader for more details.