$\tau$ physics at LHCb

We report on the first searches for lepton flavour violating $\tau^-$ decays at a hadron collider. These include searches for the lepton flavour violating decay $\tau^-\to \mu^+\mu^-\mu^-$ and the lepton flavour and baryon number violating decays $\tau^-\to \bar{p}\mu^+\mu^-$ and $\tau^-\to p\mu^-\mu^-$. Upper limits of ${\cal B}(\tau^-\to \mu^+\mu^-\mu^-) < 4.6 \times 10^{-8}$, ${\cal B}(\tau^-\to \bar{p}\mu^+\mu^-) < 3.4 \times 10^{-7}$ and ${\cal B}(\tau^-\to p\mu^-\mu^-) < 4.6 \times 10^{-7}$ are set at 90% confidence level. A measurement of the inclusive $Z\to\tau^+\tau^-$ cross-section at 7 TeV is also reported and is found to be consistent with the Standard Model. The ratio of the $Z\to\tau^+\tau^-$ cross-section to the $Z\to\mu^+\mu^-$ cross-section is found to be consistent with lepton universality.