Local-global principles for semi-integral points on Markoff orbifold pairs

In this talk we shall discuss the status of local-global principles for semi-integral points on orbifold pairs of Markoff type. If time permits, we will discuss a way to count Markoff orbifold pairs which satisfy the semi-integral Hasse principle while the corresponding Markoff surface lacks integral points. This talk is based on a joint work with Justin Uhlemann.