Ultraviolet properties of Maximal Supergravity
  We argue that recent results in string perturbation theory indicate that the four-graviton amplitude of four-dimensional N=8 supergravity might be ultraviolet finite up to eight loops. We similarly argue that the h-loop M-graviton amplitude might be finite for h<7+M/2. 
Michael B. Green (Cambridge U., DAMTP), Jorge G. Russo (ICREA,   Barcelona & Barcelona U., ECM), Pierre Vanhove (Saclay, SPhT)