  Extending the work of Ferrara and one of the authors, we present dynamical
cosmological models of $\alpha$-attractors with plateau potentials for
$3\alpha=1,2,3,4,5,6,7$. These models are motivated by geometric properties of
maximally supersymmetric theories: M-theory, superstring theory, and maximal $N
= 8$ supergravity. After a consistent truncation of maximal to minimal
supersymmetry in a seven-disk geometry, we perform a two-step procedure: 1) we
introduce a superpotential, which stabilizes the moduli of the seven-disk
geometry in a supersymmetric minimum, 2) we add a cosmological sector with a
nilpotent stabilizer, which breaks supersymmetry spontaneously and leads to a
desirable class of cosmological attractor models. These models with $n_s$
consistent with observational data, and with tensor-to-scalar ratio $r \approx
10^{-2}- 10^{-3}$, provide natural targets for future B-mode searches. We
relate the issue of stability of inflationary trajectories in these models to
tessellations of a hyperbolic geometry.

High Energy Physics - Theory;Cosmology and Nongalactic Astrophysics;General Relativity and Quantum Cosmology;High Energy Physics - Phenomenology