Title: Natural differential operators and graph complexes
Speaker: Professor Martin Markl
Speaker Info: Mathematical Institute of the Academy of Sciences of the Czech Republic
We explain how the Invariant Tensor Theorem together with an elementary representation theory reduces the problem of classifying natural differential operators into a problem formulated in terms of graph complexes. This reduced problem can then be grasped by powerful methods of homological theory of graph complexes.Date: Thursday, April 27, 2006
We believe that this combination of so far separated areas could lead to many deep and unexpected results, or at least simplify existing proofs. As an example, we give a simple proof of the fact that all natural operators on linear connections are generated by the torsion, curvature and covariant derivative. We also prove an apparently new theorem characterizing natural operations on vector fields.