**Unique Prime Decomposition Results for Equivalence Relations**

**Assistant Professor Daniel Drimbe; Department of Mathematics, University of Iowa**

Let G be a lattice in a simple connected real Lie group with finite center. The seminar work of Zimmer shows that the orbit equivalence relation R of any free ergodic probability measure preserving action of G is prime, i.e. R cannot be isomorphic to a product of equivalence relations that have infinite orbits. In my talk I will show that a product of such equivalence relations satisfies a unique prime factorization phenomenon.

This is joint work with Cyril Houdayer.