Oldenburg, den 11.06.2024
Vortragsankündigung
Im Rahmen des Oberseminars Analysis/Numerik spricht
Herr Dr. Alessandro Pietro Contini (Hannover)
über
The isomorphism of the scattering algebra
Der Vortrag findet statt am Donnerstag, 13.06.2024 von 14.30 bis 15.30 Uhr im Raum W01 0-006
Abstract:
In this talk, based on my PhD thesis, I will start by setting up the framework of the socalled scattering calculus 
. This is calculus of pseudo-differential operators on a manifold which looks like a cone near its boundary 
, metrically speaking Euclidian at infinity. Two of the main features of this algebra are: there is second filtration measuring the loss of decay near the boundary, and full ellipticity is captured by a joint principal symbol map, which, in contrast to other algebras, is fully commutative and therefore an algebra of functions of a compact manifold. Given another manifold with the same structure near the boundary, I will study the problem of classifying all the isomorphisms 
which map operators of order 
on 
to operators of order on 
. Following ideas of Duistermaat and Singer, I will show how this can be interpreted as the problem of quantising a symplectomorphism to a Fourier Integral Operator and proceed to characterise (on flat space) the isomorphisms as conjugation with such an object.
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Fakultät V
Mathematik und Naturwissenschaften