  Neutrinos are key to probing the deep structure of matter and the high-energy
Universe. Yet, until recently, their interactions had only been measured at
laboratory energies up to about 350 GeV. An opportunity to measure their
interactions at higher energies opened up with the detection of high-energy
neutrinos in IceCube, partially of astrophysical origin. Scattering off matter
inside the Earth affects the distribution of their arrival directions --- from
this, we extract the neutrino-nucleon cross section at energies from 18 TeV to
2 PeV, in four energy bins, in spite of uncertainties in the neutrino flux.
Using six years of public IceCube High-Energy Starting Events, we explicitly
show for the first time that the energy dependence of the cross section above
18 TeV agrees with the predicted softer-than-linear dependence, and reaffirm
the absence of new physics that would make the cross section rise sharply, up
to a center-of-mass energy of ~1 TeV.
