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Monday, February 29, 2016

**Abstract:** Many normal form results in differential geometry are a manifestation a rigidity phenomenon of the "structure in normal form". In this talk I will present a general local rigidity result for solutions to PDE's under the action of a closed pseudo-group of symmetries. The result is of the form: infinitesimal "tame" rigidity implies "tame" rigidity; it is in the smooth setting, and the proof uses the Nash-Moser fast convergence method. I will also discuss several classical normal form theorems in which the rigidity result applies. This is joint work with Roy Wang (PhD student at Utrecht University).