# Wave front sets of different regularity

#### 31.01.2022, 16:15  –  2.09.0.12 Forschungsseminar Differentialgeometrie

Rubens Longhi

The usual notion of wavefront set identifies the directions along which a distribution $$u$$ fails to be smooth. We present an equivalent definition that makes use of the Radon transform and which is suitable for a refinement of the notion of wavefront set. The aim is to define $$\mathcal{WF_F}$$identifying the directions along which $$u$$ fails to have a certain regularity $$\mathcal{F}$$, for example Sobolev regularity $$H^s$$ and possibly extend the theorems about the propagation of singularities to this setting.

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