On weakly mixing homeomorphisms of the two-torus that are uniformly rigid

In this paper we explore some properties of weakly mixing homeomorphisms of the two-torus that are uniformly rigid. Specifically we will show that there is a large family of weakly mixing, uniformly rigid, strictly ergodic homeomorphisms of the two-torus. Also, we will show that if a sequence of natural numbers satisfies a certain growth rate, then we can construct a weakly mixing homeomorphism of the two-torus that is uniformly rigid with respect to that sequence.