  We prove uniqueness for Calder\'on's problem with Lipschitz conductivities in
higher dimensions. Combined with the recent work of Haberman, who treated the
three and four dimensional cases, this confirms a conjecture of Uhlmann. Our
proof builds on the work of Sylvester and Uhlmann, Brown, and Haberman and
Tataru who proved uniqueness for $C^1$ conductivities and Lipschitz
conductivities sufficiently close to the identity.
