  The investigation of neutrino interactions with matter serves as a valuable
tool for understanding the fundamental structure of nucleons and potentially
uncovering novel physics phenomena. To date, the neutrino-nucleon cross section
has been examined across a range of energies spanning from a few hundred MeV to
PeV. However, the pursuit of ultra-high-energy (UHE) cosmic neutrinos,
surpassing 100 PeV in energy, holds the promise of further advancements. In the
next 10-20 years, UHE neutrino telescopes, currently in the planning stage, may
ultimately succeed in their detection. This article presents pioneering and
comprehensive estimation forecasts for the ultra-high-energy neutrino-nucleon
cross section, with a specific focus on the employment of neutrino
radio-detection within the IceCube-Gen2 experiment. The study incorporates
cutting-edge methodologies in UHE neutrino flux prediction, neutrino
propagation within the Earth, radio detection techniques, and the treatment of
background data to facilitate accurate cross section measurement projections.
Assuming the successful detection of at least a few tens of UHE
neutrino-induced events over a 10-year period, IceCube-Gen2 could achieve, for
the first time, the measurement of the cross section at center-of-mass energies
of approximately $\sqrt{s} \approx 10$--100 TeV. Furthermore, if the number of
events exceeds one hundred, the precision of the cross section measurement
could be comparable to its corresponding theoretical prediction.
