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Calabi-Yau Varieties: from Quiver Representations to Dessins d'Enfants

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arxiv 1611.09398 v1 pith:A2BWF2TX submitted 2016-11-28 math.AG hep-thmath-phmath.MPmath.NT

Yang-Hui He This is my paper · ORCID
classification math.AGhep-thmath-phmath.MPmath.NT
keywords calabi-yaugeometryphysicsrepresentationtheoryvarietieswhosealgebraic
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The connections amongst (1) quivers whose representation varieties are Calabi-Yau, (2) the combinatorics of bipartite graphs on Riemann surfaces, and (3) the geometry of mirror symmetry have engendered a rich subject at whose heart is the physics of gauge/string theories. We review the various parts of this intricate story in some depth, for a mathematical audience without assumption of any knowledge of physics, emphasizing a plethora of results residing at the intersection between algebraic geometry, representation theory and number theory.

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Cited by 1 Pith paper

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  1. Metaheuristic Generation of Brane Tilings

    hep-th 2024-12 conditional novelty 6.0 of 10

    Simulated annealing over permutation tuples can generate consistent brane tilings, yielding a 26-field example not present in catalogues that stop at 24 fields.

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