Théorique, numérique
Since its advent, string theory (ST) has been a leading candidate for a self-consistent theory of quantum gravity. Perturbative ST predicts the existence of six extra dimensions, that constitute a so-called compactification manifold. The effective description of our four-dimensional spacetime is encoded in the geometry and topology of the compactification manifolds, whose properties can be studied with the tools of G-structures. A first goal of this proposal is to classify certain SU(3) structures with torsion on toric varieties, that have several applications ranging from holography and moduli stabilisation, to the problem of scale separation and the recent Swampland program. This proposal is in the form of a co-direction between the iP2i (Physics) and the ICJ (Mathematics) of Lyon.