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.
