Strutture affini su solvarietà tre-dimensionali e simmetria speculare SYZ non-Kaehleriana

We present a new geometric construction that leads us to new examples of pairs of six-dimensional compact manifolds satisfying a non-K¨ahler version of Mirror Symmetry as formulated by Lau, Tseng, and Yau using SU(3)-structures. In this new setting, the Calabi-Yau geometry is replaced by the symplectic half-flat geometry on the IIA-side and by the complex-balanced geometry on the IIB-side. The link between the two is provided by the Strominger-Yau-Zaslow construction which relies on the presence of a third space B over which the IIA-side fibers in Lagrangian tori. We will show how to build these examples using the theory of solvmanifolds and how it is linked to the affine geometry of the base of the fibration. Finally, we will describe the action of the Fourier-Mukai transform on semi-flat differential forms and how it realizes the equivalence of the Tseng-Yau cohomology on the IIA-side with the Bott-Chern cohomology on the IIB-side.