08.05.2025, 16:15
– Haus 9, Raum 1.22
Forschungsseminar Differentialgeometrie
Scalar Curvature Rigidity and Higher Index Theory
Thomas Tony
Onirban Islam
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 scalar pseudodifferential operators of real-principal type on a boundaryless manifold can be always microlocalised to the partial derivative. On a manifold with boundary, an analogue of this result is due to Melrose for scalar b-pseudodifferential operators. In this talk, I shall explain these notions, in particular, the generalisation in the bundle setting. Then, I shall sketch how to incorporate boundary conditions using the so-called third Green's identity and single-layer potential.