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- W4300783384 abstract "Following an idea of Ozawa, we give a new proof of Kazhdan's property (T) for ${rm SL}(3,mathbb Z)$, by showing that $Delta^2- frac{1}{6} Delta$ is a hermitian sum of squares in the group algebra, where $Delta$ is the unnormalized Laplace operator with respect to the natural generating set. This corresponds to a spectral gap of $frac{1}{72}sim 0.014$ for the associated random walk operator. The sum of squares representation was found numerically by a semidefinite programming algorithm, and then turned into an exact symbolic representation, provided in an attached Mathematica file." @default.
- W4300783384 created "2022-10-04" @default.
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- W4300783384 date "2014-11-10" @default.
- W4300783384 modified "2023-10-06" @default.
- W4300783384 title "Kazhdan's Property (T) via Semidefinite Optimization" @default.
- W4300783384 doi "https://doi.org/10.48550/arxiv.1411.2488" @default.
- W4300783384 hasPublicationYear "2014" @default.
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