Probing ultra-high-energy neutrinos with the IceCube-Gen2 in-ice radio array

The next generation neutrino telescope, IceCube-Gen2, will be sensitive to the astrophysical and cosmogenic flux of neutrinos across a broad energy range, from the TeV to the EeV scale. The planned design includes 8 cubic kilometers of ice instrumented with approximately 10,000 optical sensors, a surface array, and a radio array of antennas embedded in the ice laid out sparsely over 500 km$^2$. The radio array provides sensitivity to ultra-high energy neutrinos using independent radio stations that can trigger on Askaryan emission from neutrino interactions in the ice. In this contribution, we present the design for the radio array along with its planned implementation, which is expected to increase sensitivity to neutrinos with energies beyond 100 PeV by at least an order of magnitude over existing arrays. Furthermore, we will quantify the expected science output by presenting measurement forecasts for the main science cases of diffuse flux and point source discovery, as well as cross-section and flavor measurements.