String topology studies the algebraic structure of the homology of the free loop space of a manifold. I'll describe joint work with Nathalie Wahl about string topology operations, and about what these operations compute.  We have simplified, chain-level definitions for the "loop" or "string" product and coproduct. The new definitions make possible new links between geometry and loop products. For example, If the k-fold coproduct of a homology class X on LM is nontrivial, then every representative of X contains a loop with a (k+1)-fold self-intersection.
    If time permits I will discuss homotopy invariance of the coproduct (joint with Nathalie Wahl) and symmetry in the free loop space (with Kai Cieliebak and Alex Oancea).
    The talk will emphasize geometric motivation and examples. No knowledge of loop products or string topology will be assumed.