M-theory, black holes and cosmology.

This paper is dedicated to Michael J. Duff on the occasion of his 70th birthday. I discuss some issues of M-theory/string theory/supergravity closely related to Mike's interests. I describe a relation between STU black hole entropy, the Cayley hyperdeterminant, the Bhargava cube and a three-qubit Alice-Bob-Charlie triality symmetry. I shortly describe my recent work with Gunaydin, Linde and Yamada on M-theory cosmology (Gunaydin 2020 M-theory cosmology, octonions, error-correcting codes (http://arxiv.org/abs/2008.01494)), inspired by the work of Duff with Ferrara and Borsten, Levay, Marrani Here, we have seven-qubits, a party including Alice, Bob, Charlie, Daisy, Emma, Fred and George. Octonions and Hamming error-correcting codes are at the base of these models. They lead to seven benchmark targets of future cosmic microwave background missions looking for primordial gravitational waves from inflation. I also show puzzling relations between the fermion mass eigenvalues in these cosmological models, the exceptional Jordan eigenvalue problem and black hole entropy. The symmetry of our cosmological models is illustrated by beautiful pictures of a Coxeter projection of the root system of E7.