Abstract: An empty simplex is a lattice simplex in which vertices are the only lattice points. We show two constructions leading to the first known empty simplices of width larger than their dimension: - We introduce cyclotomic simplices and exhaustively compute all the cyclotomic simplices of dimension 10 and volume up to 231. Among them, we find five empty ones of width 11 and none of larger width. - Using circulant matrices of a very specific form, we construct empty simplices of arbitrary dimension d and width growing asymptotically as d/arcsinh(1) ~ 1.1346 d.

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