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

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This work summarises recent progress obtained by the mini-superpspace quantization of N=1, d=4 supergravity, formulated in the framework of the Bianchi IX cosmological model. The emphasis is put on three main results: the completeness of the solution space obtained, the elements suggesting a hidden Kac-Moody structure of the theory and those leading to conjecture an avoidance of the cosmological singularity by some branches of the wave function of the Universe.