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We study compactification of 6 dimensional (1,0) theories on T^2. We usegeometric engineering of these theories via F-theory and employ mirror symmetrytechnology to solve for the effective 4d N=2 geometry for a large number of the(1,0) theories including those associated with conformal matter. Using this weshow that for a given 6d theory we can obtain many inequivalent 4d N=2 SCFTs.Some of these respect the global symmetries of the 6d theory while othersexhibit SL(2,Z) duality symmetry inherited from global diffeomorphisms of theT^2. This construction also explains the 6d origin of moduli space of 4d affineADE quiver theories as flat ADE connections on T^2. Among the resulting 4d N=2CFTs we find theories whose vacuum geometry is captured by an LG theory (asopposed to a curve or a local CY geometry). We obtain arbitrary genus curves ofclass S with punctures from toroidal compactification of (1,0) SCFTs where thecurve of the class S theory emerges through mirror symmetry. We also show thattoroidal compactification of the little string version of these theories canlead to class S theories with no punctures on arbitrary genus Riemann surface.

Geometric Engineering, Mirror Symmetry and 6d (1,0) -> 4d, N=2