  The transport of gas towards the centre of galaxies is critical for black
hole feeding and, indirectly, it can control active galactic nucleus (AGN)
feedback. We have quantified the molecular gas inflow in the central R<1kpc of
M51 to be 1 Msun/yr, using a new gravitational torque map and the molecular gas
traced by the PdBI Arcsecond Whirlpool Survey (PAWS). The nuclear stellar bar
is responsible for this gas inflow. We have also used torque profiles to
estimate the location of dynamical resonances, suggesting a corotation for the
bar at R~20", and a corotation for the spiral at R~100". We demonstrate how
important it is to correct 3.6um images for dust emission in order to compute
gravitational torques, and we carefully examine further sources of uncertainty.
Our observational measurement of gas inflow can be compared with nuclear
molecular outflow rates and provide useful constraints for numerical
simulations.
