  We discuss torsional oscillations of highly magnetised neutron stars
(magnetars) using two-dimensional, magneto-elastic-hydrodynamical simulations.
Our model is able to explain both the low- and high-frequency quasi-periodic
oscillations (QPOs) observed in magnetars. The analysis of these oscillations
provides constraints on the breakout magnetic-field strength, on the
fundamental QPO frequency, and on the frequency of a particularly excited
overtone. More importantly, we show how to use this information to generically
constraint properties of high-density matter in neutron stars, employing
Bayesian analysis. In spite of current uncertainties and computational
approximations, our model-dependent Bayesian posterior estimates for SGR
1806-20 yield a magnetic-field strength $\bar B\sim
2.1^{+1.3}_{-1.0}\times10^{15}\,$G and a crust thickness of $\Delta r =
1.6^{+0.7}_{-0.6}$ km, which are both in remarkable agreement with
observational and theoretical expectations, respectively (1-$\sigma$ error bars
are indicated). Our posteriors also favour the presence of a superfluid phase
in the core, a relatively low stellar compactness, $M/R<0.19$, indicating a
relatively stiff equation of state and/or low mass neutron star, and high shear
speeds at the base of the crust, $c_s>1.4\times10^8\,$cm/s. Although the
procedure laid out here still has large uncertainties, these constraints could
become tighter when additional observations become available.
