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Minimal surfaces in spheres and random permutations

Recent progress on geometric analysis and Riemannian geometry October 21, 2024 - October 25, 2024

October 22, 2024 (03:30 PM PDT - 04:30 PM PDT)
Speaker(s): Antoine Song (California Institute of Technology)
Location: SLMath: Eisenbud Auditorium, Online/Virtual
Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC
Video

Minimal surfaces in spheres and random permutations

Abstract

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Minimal surfaces in spheres, which are invariant by a group of symmetries, are closely related to group theory, hyperbolic geometry and geometric topology. In this talk, I will discuss a new connection with random matrices. As we will explain, from two permutations, one can associate a 2d minimal surface in a Euclidean sphere. The main property is a probabilistic rigidity phenomenon: if the two permutations are chosen uniformly at random, then with high probability, the minimal surface has a geometry close to that of the hyperbolic plane.

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Minimal surfaces in spheres and random permutations

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