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2025 IHES Summer School – Statistical Aspects of Nonlinear Physics
27 videos

2025 IHES Summer School – Statistical Aspects of Nonlinear Physics

AGCT 2025 - Arithmetic, Geometry, Cryptography and Coding Theory / AGCT 2025 - Arithmétique, Géométrie, Cryptographie et Théorie des Codes
6 videos

AGCT 2025 - Arithmetic, Geometry, Cryptography and Coding Theory / AGCT 2025 - Arithmétique, Géométrie, Cryptographie et Théorie des Codes

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5 videos

Perfectly matched perspectives on statistical mechanics, combinatorics and geometry / Perspectives couplées sur la mécanique statistique, la combinatoire et la géométrie

Fuzzy Sphere Meets Conformal Bootstrap 2025
20 videos

Fuzzy Sphere Meets Conformal Bootstrap 2025

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2025 - T2 - WS2 - Low-dimensional phenomena: geometry and dynamics

Collection 2025 - T2 - WS2 - Low-dimensional phenomena: geometry and dynamics

Organizer(s) Bromberg, Kenneth ; Haïssinsky, Peter ; Hamenstädt, Ursula ; Maloni, Sara ; Sambarino, Andrés ; Schapira, Barbara
Date(s) 23/06/2025 - 27/06/2025
linked URL https://indico.math.cnrs.fr/event/11570/
2 17

Selberg, Ihara and Berkovich

By Wenyu Pan

We use the Selberg zeta function to study the limit behavior of resonances of a degenerating family of Kleinian Schottky groups. We prove that, after a suitable rescaling, the Selberg zeta functions converge to the Ihara zeta function of a limiting finite graph associated with the relevant non-Archimedean Schottky group acting on the Berkovich projective line.

An application of our techniques is to obtain an exponential error term about the asymptotics for the vanishing rate of the Hausdorff dimension of limit sets of certain degenerating Schottky groups generating symmetric three-funnel surfaces. Here, one key idea is to introduce an intermediate zeta function that captures both Archimedean and non-Archimedean information (while the traditional Selberg resp. Ihara zeta function concerns only Archimedean resp. non-Archimedean properties). This is a joint work with Jialun Li, Carlos Matheus, and Zhongkai Tao.

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