Causality, observables, and algebras

I will overview one way of describing algebraic structures: operads.  I will provide multitudinous examples before introducing a new class of algebraic objects defined on Lorentzian manifolds.  Such spaces have a notion of causality, and these algebras take that into account.  Finally, I will mention how these causal algebras are related to topological theory on Euclidean space via Wick rotation, i.e., the Wightman distributions associated to a Euclidean topological field theory are a causal algebra.

I hope to use the majority of the talk discussing h-principles.  I hope to explain an alternative proof of a large class of h-principles, which can be applied to spaces of embeddings, thereby proving the Tangle Hypothesis.