Shimura and Teichmüller curves

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Braid groups and Hodge theory (2013, background): “Möller shows V is the only subvariety of any moduli space Mg, g ≥ 2 which is both a Shimura curve and a Teichmüller curve [Mo] Irregular covers of elliptic curves.”
SQUARE-TILED CYCLIC COVERS (2010, background): “Möller conjectured in [30] that these two examples are the only Teichmüller curves with maximally degenerate Kontsevich–Zorich spectra.”
On totally geodesic submanifolds in the Jacobian locus (2013, result): “For results on Shimura subvarieties contained in j(Mg) we refer to [13, 20, 22, 25, 21, 1, 19, 15, 18].”
The Torelli locus and special subvarieties (2011, background): “It is shown in [41] that for g = 2 and g ≥ 6 there are no such curves.”
Nonvarying sums of Lyapunov exponents of Abelian differentials in low genus (2011, background): “2745// (see [22; 37]), generates a Teichmüller curve C with L.”
Cyclic Coverings, Calabi-Yau Manifolds and Complex Multiplication (2007, background): “Möller [41], which provides the example of the next section.”