ON MASAS OF THE CALKIN ALGEBRA

Speaker(s)

PIOTR KOSZMIDER

Affiliation

IMPAN, Warszawa, Poland

Language of the talk

English

Date

Oct. 7, 2026, 5:15 p.m.

Title in Polish

ON MASAS OF THE CALKIN ALGEBRA

Seminar

North Atlantic Noncommutative Geometry Seminar

Masas of the Calkin algebra have proved considerably more elusive than masas of the algebra of bounded operators on a separable Hilbert space. Classical liftable masas fall into only three isomorphism types, while nonliftable examples suggest a much richer picture. I will survey classical results on masas of the Calkin algebra and discuss my recent results. Assuming the Continuum Hypothesis, projection-generated masas admit a complete isomorphic classification: C(K) is *-isomorphic to such a masa precisely when K is compact Hausdorff, totally disconnected, has weight at most the continuum and has no G-delta points. We thus arrive at masas which are group C*-algebras, nonseparable von Neumann algebras, masas admitting conditional expectations and others admitting none, as well as many other exotic examples. Even in ZFC, we can obtain a large family of pairwise nonisomorphic projection-generated masas. I will also discuss recent results showing that the possible densities of masas may depend on additional set-theoretic assumptions, and how the Continuum Hypothesis characterisation may consistently fail. The talk is based on two preprints: arXiv:2512.06580 and arXiv:2609.12916