Test of lepton universality and searches for lepton flavor violation at BaBar

The BaBar experiment has recently obtained some important results in the search for new physics in leptonic and lepton flavor violating decays, exploiting the complete datasets collected at the $\Upsilon(4S)$, $\Upsilon(3S)$ and $\Upsilon(2S)$ energies. In particular, new limits on the ratio $\Gamma(\Upsilon(1S)\to\tau^+\tau^-)/\Gamma(\Upsilon(1S)\to\mu^+\mu^-)$, on lepton flavor violating decays of the $\Upsilon(3S)$ and $\Upsilon(2S)$, and on $\tau$ decays to three charged leptons or $\tau\to e/\mu \gamma$ are presented.