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The roundabout form of intersection underwent a huge boom in Switzerland in the 1990s. So-called compact roundabouts have proved particularly successful with regard to traffic safety; in many cases it was possible to eliminate accident "black spots" by converting existing intersections. Analysis of accident data has shown, however, that safety improvements have not produced satisfactory results at all roundabouts. Indeed, before-and-after comparisons indicate certain roundabouts actually experienced increases in the number of accidents. The causes of these negative effects appear to lie in local circumstances. A research project was launched to investigate the relationships between accident occurrence, traffic flow, and geometry in the area of roundabouts. The goal of the project was to develop basic principles for a Swiss design standard. The central importance in roundabout design of the deflection of vehicle pass-through tracks by means of the roundabout's central island was established. An insufficient deflection of the vehicle stream from the straight direction of travel results in failures to give way, increased pass-through speeds, and underestimations of these speeds by the other parties in conflict situations. These consequences are manifested in increased accident frequency.

In this article we construct Laurent polynomial Landau-Ginzburg models for cominuscule homogeneous spaces. These Laurent polynomial potentials are defined on a particular algebraic torus inside the Lie-theoretic mirror model constructed for arbitrary homogeneous spaces in [Rie08]. The Laurent polynomial takes a similar shape to the one given in [Giv96] for projective complete intersections, i.e. it is the sum of the toric coordinates plus a quantum term. We also give a general enumeration method for the summands in the quantum term of the potential in terms of the quiver introduced in [CMP08], associated to the Langlands dual homogeneous space. This enumeration method generalizes the use of Young diagrams for Grassmannians and Lagrangian Grassmannians and can be defined typeindependently. The obtained Laurent polynomials coincide with the results obtained so far in [PRW16] and [PR13] for quadrics and Lagrangian Grassmannians. We also obtain new Laurent polynomial Landau-Ginzburg models for orthogonal Grassmannians, the Cayley plane and the Freudenthal variety.

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