LFV in tau and muon decays within SUSY seesaw

In these proceedings we present the results for lepton flavour violating tau and muon decays within the SUSY seesaw scenario. Specifically, we consider the Constrained Minimal Supersymmetric Standard Model extended by three right handed neutrinos, $\nu_{R_i}$ and their corresponding SUSY partners, ${\tilde \nu}_{R_i}$, ($i=1,2,3$), and use the seesaw mechanism for neutrino mass generation. We include the predictions for the branching ratios of two types of lepton flavour violating channels, $l_j \to \l_i \gamma$ and $l_j \to 3 l_i$, and compare them with the present bounds and future experimental sensitivities. We first analyse the dependence of the branching ratios with the most relevant SUSY seesaw parameters, and we then focus on the particular sensitivity to $\theta_{13}$, which we find specially interesting on the light of its potential future measurement. We further study the constraints from the requirement of successfully producing the baryon asymmetry of the Universe via thermal leptogenesis, which is another appealing feature of the SUSY seesaw scenario. We conclude with the impact that a potential measurement of $\theta_{13}$ can have on lepton flavour violating physics. This is a very short summary of the works in Refs. \cite{Arganda:2005ji} and \cite{Antusch:2006vw} to which we refer the reader for more details.