  The notion of age of elements of complex linear groups was introduced by M.
Reid and is of importance in algebraic geometry, in particular in the study of
crepant resolutions and of quotients of Calabi-Yau varieties. In this paper, we
solve a problem raised by J. Kollar and M. Larsen on the structure of finite
irreducible linear groups generated by elements of age at most 1. More
generally, we bound the dimension of finite irreducible linear groups generated
by elements of bounded deviation. As a consequence of our main results, we
derive some properties of symmetric spaces for the unitayr group having
shortest closed geodesics of bounded length, and of quotients of affine space
by a finite group having a crepant resolution.
