2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/142901Group field theories are a new type of field theories over group manifolds and a generalization of matrix models, that have recently attracted much interest in quantum gravity research. They represent a development of and a possible link between different approaches such as loop quantum gravity and simplicial quantum gravity. After a brief introduction to the GFT formalism we put forward a long but still far from exhaustive list of open issues that this line of research faces, and that could be represent interesting challenges for mathematicians and mathematical physicists alike.16 pages, 7 figures; RevTex4; to appear in the proceedings of the Conference on Combinatorics and Physics, MPIM Bonn, March 19-23, 2007High Energy Physics - TheoryGeneral Relativity and Quantum Cosmologytext