NONCOMMUTATIVE GEOMETRY ON THE BERKOVICH PROJECTIVE LINE

Speaker(s)

MASOUD KHALKHALI

Affiliation

Western University, London, Ontario, Canada

Language of the talk

English

Date

June 10, 2026, 5:15 p.m.

Information about the event

ZOOM

Title in Polish

NONCOMMUTATIVE GEOMETRY ON THE BERKOVICH PROJECTIVE LINE

Seminar

North Atlantic Noncommutative Geometry Seminar

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We discuss recent joint work with Damien Tageddine (J. Fractal Geom. 13, 2026) on noncommutative geometric structures associated to the Berkovich projective line. Starting from the action of p-adic Schottky groups, we construct Patterson-Sullivan measures on the boundary of the Berkovich projective line and study their critical exponents. We then show that these measures give rise to KMS states on naturally associated crossed product C*-algebras, with the critical exponent appearing as the inverse temperature. The resulting framework connects Berkovich rigid analytic geometry to noncommutative geometry, hyperbolic group actions, operator algebras, and quantum statistical mechanics in the non-Archimedean setting.

 

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