THE log-LAPLACIAN ON AHLFORS REGULAR SPACES AND NONCOMMUTATIVE BOUNDARIES

Speaker(s)

DIMITRIS M. GERONTOGIANNIS

Affiliation

IMPAN, Warszawa, Poland

Language of the talk

English

Date

Nov. 27, 2024, 5:15 p.m.

Link

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

Information about the event

IMPAN room 405 & ZOOM

Title in Polish

THE log-LAPLACIAN ON AHLFORS REGULAR SPACES AND NONCOMMUTATIVE BOUNDARIES

Seminar

North Atlantic Noncommutative Geometry Seminar

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The Laplace-Beltrami operator is a fundamental tool in the study of compact Riemannian manifolds. In this talk, based on joint work with Bram Mesland (Leiden), I will introduce the logarithmic analogue of this operator on Ahlfors regular spaces. These are metric-measure spaces that might lack any differential or algebraic structure. Examples are compact Riemannian manifolds, several fractals, self-similar Smale spaces and limit sets of hyperbolic isometry groups. Further, this operator is intrinsically defined, its spectral properties are analogous to those of elliptic pseudo-differential operators on manifolds, and it exhibits compatibility with non-isometric actions in the sense of noncommutative geometry. If time allows, I will also discuss the recent joint work with Magnus Goffeng (Lund) and Bram Mesland on applying the log-Laplacian to study the spectral geometry of Cuntz-Krieger algebras using heat operators and isometry groups.

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