AUTOMORPHISMS OF THE BOUTET DE MONVEL ALGEBRA

Prelegent(ci)

RYSZARD NEST

Afiliacja

Københavns Universitet, Denmark

Język referatu

angielski

Termin

15 stycznia 2025 17:15

Link

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

Informacje na temat wydarzenia

IMPAN 405 & ZOOM

Tytuł w języku polskim

AUTOMORPHISMS OF THE BOUTET DE MONVEL ALGEBRA

Seminarium

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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