Mathematics Colloquia and Seminars

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Description

Spherical knot n-mosaics represent knot diagrams on the surface of a cube by tiling each face with an n×n grid using a set of 11 tile types and connecting the diagram across faces. This construction provides a natural three-dimensional realization of knot diagrams and leads to new knot invariants. We study the minimal integer n for which a knot admits such a representation, provide explicit computations for knots with crossing number at most 8, and establish bounds for knots with higher crossing number. We also discuss face-efficient spherical knot mosaics, which minimize the number of cube faces used. We construct face-efficient spherical knot n-mosaics for all knots with crossing number at most 8 and establish bounds for knots with higher crossing number.