Studies of Hadronic Interactions at Ultra-high Energies with the Pierre Auger Observatory

The hybrid design of the Pierre Auger Observatory allows one to measure the longitudinal profile of ultra-high energy air showers and the depth at which the shower reaches its maximum size, Xmax. It also provides a record of the shower front by sampling the secondary particles at ground level. These measurements give a variety of independent experimental observables with information about the nature of the primary particle and its interactions. In this contribution we present a comparison of our mass sensitive observables with the prediction of different hadronic interaction models. Furthermore we show how the analysis of the tail of the distribution of Xmax allows one to estimate the proton-air cross-section for particle production at center-of-mass energies of 57 TeV.