He constructed a pair of flat tori of 16 dimension, using arithmetic lattices first studied by Ernst Witt.
Among his numerous contributions, the most famous one is a general construction of isospectral manifolds (1985), which is based on his geometric model of number theory, and is considered to be a breakthrough in the problem proposed by Mark Kac in "Can one hear the shape of a drum?" (see Hearing the shape of a drum).