Extensive air showers are complex objects, resulting of billions of
particle reactions initiated by single cosmic ray at ultra-high-energy.
Their characteristics are sensitive both to the mass of the primary
cosmic ray and to the details of hadronic interactions. Many of the
interactions that determine the shower features occur in energy and kinematic
regions beyond those tested by human-made accelerators.
We will report on the measurement of the proton-air cross
section for particle production at a center-of-mass energy per nucleon
of 39 TeV and 56 TeV. We will also show comparisons of post-LHC hadronic
interaction models with shower data by studying the
moments of the distribution of the depth of the electromagnetic maximum,
the number and production depth of muons in air showers, and finally a
parameter based on the rise-time of the surface detector signal,
sensitive to the electromagnetic and muonic component of the shower.
While there is good agreement found for observables based on the
electromagnetic shower component, discrepancies are observed for