Trickle-down Theorems for High-dimensional Expanders via Log-concave Polynomials

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Trickle-Down in Localization Schemes

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From local discrete curvature notions of graphs to global properties of the underlying spaces

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Property (T), sums of square and numerical certificates

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Aldous-type Spectral Gaps in Unitary Groups

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Random unitary circuits with constant spectral gap

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Entropic independence

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Field dynamics and its applications

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Spectral gap of 1D quantum Gibbs samplers

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Convex-body Sampling to the Kannan-Lovász-Simonovits Conjecture

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