Lattice QCD results on soft and hard probes of strongly interacting matter

Abstract: We present recent results from lattice QCD relevant for the study of strongly interacting matter as it is produced in heavy ion collision experiments. The equation of state at non-vanishing density from a Taylor expansion up to $6^{th}$ order will be discussed for a strangeness neutral system and using the expansion coefficients of the series limits on the critical point are estimated. Chemical freeze-out temperatures from the STAR and ALICE Collaborations will be compared to lines of constant physics calculated from the Taylor expansion of QCD bulk thermodynamic quantities. We show that qualitative features of the $\sqrt{s_{NN}}$ dependence of skewness and kurtosis ratios of net proton-number fluctuations measured by the STAR Collaboration can be understood from QCD results for cumulants of conserved baryon-number fluctuations. As an example for recent progress towards the determination of spectral and transport properties of the QGP from lattice QCD, we will present constraints on the thermal photon rate determined from a spectral reconstruction of continuum extrapolated lattice correlation functions in combination with input from most recent perturbative calculations.