METRIC LIMITS OF SPECTRAL TRIPLES AND NONCOMMUTATIVE PRINCIPAL G-BUNDLES

Speaker(s)

CARLA FARSI

Affiliation

University of Colorado, Boulder, USA

Language of the talk

English

Date

Jan. 22, 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

METRIC LIMITS OF SPECTRAL TRIPLES AND NONCOMMUTATIVE PRINCIPAL G-BUNDLES

Seminar

North Atlantic Noncommutative Geometry Seminar

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The spectral propinquity, a generalization of the Gromov-Hausdorff distance to the realm of noncommutative geometry, is a distance on metric spectral triples developed within the framework of metric noncommutative geometry by Latrémolière. Metric spectral triples have the property that they induce the weak-* topology on the state space of the associated (unital) C*-algebras. The convergence of spectral triples for the spectral propinquity implies the convergence of the geometry content of the relevant spectral triples as well. We will give a general convergence theorem and its various applications to situations when a (noncommutative) space “collapses” to another space. In these cases, the spectrum of the Dirac operators on the collapsed spaces is the limit of the spectra of the Dirac operators on the collapsing families of (noncommutative) spaces. The functional calculus also converges. Particular examples are given by noncommutative principal G-bundles associated with a free action (in the sense of Ellwood) of a compact Lie group G.

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