AUTOMORPHISMS OF THE BOUTET DE MONVEL ALGEBRA

Speaker(s)

RYSZARD NEST

Affiliation

Københavns Universitet, Denmark

Language of the talk

English

Date

Jan. 15, 2025, 5:15 p.m.

Link

https://uw-edu-pl.zoom.us/j/95105055663?pwd=TTIvVkxmMndhaHpqMFUrdm8xbzlHdz09

Information about the event

IMPAN 405 & ZOOM

Title in Polish

AUTOMORPHISMS OF THE BOUTET DE MONVEL ALGEBRA

Seminar

North Atlantic Noncommutative Geometry Seminar

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In a remarkable work in 1976, Duistermaat and Singer studied the algebras of all classical pseudodifferential operators on smooth boundaryless manifolds. They gave a description of order-preserving algebra isomorphism between the algebras of classical pseudodifferential operators of two manifolds. The subject of this talk is a generalisation of their results to manifolds with boundary. The algebra of pseudodifferential operators that we are interested in plays the role of the Boutet de Monvel algebra. What appears in the study of automorphisms are Fourier integral operators. We will try to explain their appearance both in the boundaryless and the boundary case. As it turns out, the non-trivial boundary case introduces both complications and simplifications of the involved analysis. The analysis that we need in the next step mostly reduces to relatively classical results about automorphisms and homology of the Toeplitz algebra, and basic facts from K-theory. Based on joint work in progress with Elmar Schrohe.

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