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This work summarises recent progress obtained by the mini-superpspacequantization of $\mathcal N=1$, $d=4$ supergravity, formulated in the frameworkof the Bianchi IX cosmological model. The emphasis is put on three main results: the completeness of the solution space obtained, the elements suggesting ahidden Kac-Moody structure of the theory and those leading to conjecture anavoidance of the cosmological singularity by some branches of the wave functionof the Universe.

Minisuperspace quantum supersymmetric cosmology (and its hidden hyperbolic Kac-Moody structures)