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The Geometry of Spherical Spin GlassesSpherical spin glasses are random energy functions on the sphere in high-dimensional Euclidean space, originally introduced in physics as theoretical models for disordered magnetic materials. I will present geometric descriptions of their Gibbs measures that relate their asymptotic support to structural features of the energy landscape (such as bands around critical points or approximate maximizers at certain special radii). I will briefly mention how these geometric descriptions relate to and complement the Parisi theory and how they are used both to make rigorous and to generalize certain predictions from the Thouless-Anderson-Palmer approach. Finally, I will explain how these geometric results recently led to optimization algorithms and algorithms for solving random polynomial systems that are provably optimal within a natural class of stable algorithms.Uploaded 07-10-26 Learn more about your ad choices. Visit megaphone.fm/adchoices
