pairs of Calabi-Yau type algebraic spaces , which give rise to the same quantum superstring theory. Evoking the fantasy world of JK Rowling, two spaces would be symmetrical if they project the same image in the Mirror of Erised . Conjecturally, this type of symmetry extends to the world of complex non-algebraic spaces, relating pairs of solutions of the Hull-Strominger equations. Simple solutions Mario García-Fernández’s work, recently published in the Journal für die reine und angewandte Mathematik , consists of two different parts. In the first part, the author constructs new examples of solutions of the Hull-Strominger system in non-algebraic Calabi-Yau type spaces. Using a natural ansatz for solutions, García-Fernández shows that the existence of

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solutions is reduced to algebraic criteria (which come Ivory Coast WhatsApp Number List from the Theory of Geometric Invariants introduced by D. Mumford) combined with elementary analytical methods. His solutions are comparatively much simpler than those found by J.-X. Fu and Shing-Tung Yau by means of the complex Monge-Ampère equation. Qualitative properties In the second part, García-Fernández’s work studies qualitative properties of the new solutions found in relation to the conjectural proposal of Mirror Symmetry of type (0,2) for complex non-algebraic spaces . To do this, the author proves that his solutions appear in related pairs by means of Topological T-duality, a geometric version of the T-duality relationship between quantum field theories

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discovered in physics in the mid-1980s. Its construction provides the first examples of T-dual solutions of the Hull-Strominger system in non-algebraic complex manifolds, and natural candidates for pairs with mirror symmetry. First examples Based on this research, García-Fernández together with researchers L. Alvarez-Consul and Andoni de Arriba de La Hera from the Institute of Mathematical Sciences (CSIC-UAM-UC3M-UCM), have found in a recent preprint (repository arXiv: 2012.01851 , in evaluation) the first examples of non-algebraic spaces related by Mirror Symmetry of type (0,2). This finding has been achieved by means of a detailed study of the geometry of the throat of wormholes in the theory of superstrings, caused by the presence of an

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