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Let S be an ergodic measure-preserving automorphism on a non-atomicprobability space, and let T be the time-one map of a topologically weak mixingsuspension flow over an irreducible subshift of finite type under a Holderceiling function. We show that if the measure-theoretic entropy of S isstrictly less than the topological entropy of T, then there exists an embeddingfrom the measure-preserving automorphism into the suspension flow. As acorollary of this result and the symbolic dynamics for geodesic flows oncompact surfaces of negative curvature developed by Bowen and Ratner, we alsoobtain an embedding from the measure-preserving automorphism into a geodesicflow, whenever the measure-theoretic entropy of S is strictly less than thetopological entropy of the time-one map of the geodesic flow.

Weak mixing suspension flows over shifts of finite type are universal