### Speaker

### Description

We report on the most recent results of studies of tau-lepton decays, relying on about $430\times10^6$ $e^+e^- \to \tau^+\tau^-$ events produced at a center-of-mass energy near 10.6 GeV with the BABAR detector at the PEP-II $e^+e^-$ collider.

We present measurements of the branching fractions and the spectral functions for the processes $\tau^{-}\to K^{-}K_S (\pi^{0}) \nu_\tau$, which can be used to determine the hadronic contribution to the muon $g-2$ due to the vacuum polarization.

We present also measurements of the branching fractions of the processes $\tau^{-}\to K^{-} n\pi^{0}\nu_\tau$, with n=1,2,3, which can be used to improve the determination of $|V_{us}|$ from the branching fraction $\tau^{-} \to X_{s} \nu_\tau$ computed as the sum of all measured exclusive modes with a method based on finite-energy QCD sum rules.