The project is based on our research (Ryom and Treves, Phys Rev X Life, 2023, and unpublished) and on extensive data on language parameters collected by Longobardi and collaborators (Ceolin et al, Phil Trans Roy Soc B, 2021) which suggest that language diversity may reflect the disordered freezing dynamics that in a spin glass leads to a multiplicity of ground states. In a simplified model, vectors of binary syntactic parameters interact via strong asymmetric logical implications and weak partly symmetric influences, which can produce critical slowing down through a novel mechanism of percolated freezing. Candidates should be keen to develop new mathematical and computational approaches, as sketched in https://arxiv.org/abs/2307.03152 or otherwise, and enjoy learning about issues and narratives in scientific communities other than their own.