  Gromov conjectured that any irreducible lattice in a symmetric space of rank
at least 3 should have at most polynomial Dehn function. We prove that the
lattice Sp(2p;Z) has quadratic Dehn function when p is at least 5. By results
of Broaddus, Farb, and Putman, this implies that the Torelli group in large
genus is at most exponentially distorted.
