We study the propagation of intense, high repetition rate laser pulses of picosecond duration at 1.03 µm central wavelength through air. Evidence of filamentation is obtained from measurements of the beam profile as a function of distance, from photoemission imaging and from spatially resolved sonometric recordings. Good agreement is found with numerical simulations. Simulations reveal an important self shortening of the pulse duration, suggesting that laser pulses with few optical cycles could be obtained via double filamentation. An important lowering of the voltage required to induce guided electric discharges between charged electrodes is measured at high laser pulse repetition rate.