Simulated annealing over permutation tuples can generate consistent brane tilings, yielding a 26-field example not present in catalogues that stop at 24 fields.
Calabi-Yau Varieties: from Quiver Representations to Dessins d'Enfants
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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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Metaheuristic Generation of Brane Tilings
Simulated annealing over permutation tuples can generate consistent brane tilings, yielding a 26-field example not present in catalogues that stop at 24 fields.