An introduction to microlocalisation on a manifold with boundary

09.11.2023, 16:00  –  Haus 9, Raum 0.14
Forschungsseminar Differentialgeometrie

Onirban Islam (UP)

Loosely speaking, if two (pseudo)differential operators differ only by smoothing operators then they are called microlocal conjugate to each other. It is a classic result by Duistermaat and Hörmander that an appropriate scalar pseudodifferential operator on a boundaryless manifold can be always microlocalised to the partial derivative. On a manifold with boundary, the analogue of this result is due to Melrose. Technically this is expressed in terms of the so-called b-wavefront set which captures the notion of the position and direction of singularities of a distribution on a manifold with boundary. In this talk, I shall give an introduction to the b-calculus pertinent to microlocalisation.