Invitation to Random Tensor Models: from random geometry, enumeration of tensor invariants, to characteristic polynomials

I will introduce random tensor models by first reviewing their motivation coming from random geometric approach to quantum gravity. Then, I will selectively present some of the interesting research results, by highlighting recent results on enumeration of graphs representing tensor invariants, and reporting our recent work on a new notion of characteristic polynomials for tensors via Grassmann integrals and distributions of roots of random tensors. The latter two are based on arXiv:2404.16404[hep-th] and arXiv:2510.04068[math-ph]