Stabilization hypothesis and higher braided operads

The stabilization hypothesis of Breen,Baez and Dolan states that k-fold monoidal n-category is "the same" as (k+1)-fold (and therefore $\infty$-fold) monoidal n-category if k is grater or equal to n+2. In the first half of my talk I will explain this hypothesis in an informal manner and I will relate it to the geometry of configuration spaces of k points in $R^n$. In somewhat more technical second half I will introduce n-braided operads and will give a sketch of a proof of a stabilization theorem for n-braided operads. The BBD stabilization hypothesis is an easy corollary from this statement.