In the second talk we give various examples of how the relationship between Mac Lane valuations and models of the projective line can be used to resolve singularities and find regular models of arithmetic surfaces. In particular, we will overview how Mac Lane valuations can be used to give explicit minimal regular normal crossings models of superelliptic curves (joint with Padmavathi Srinivasan), and also how they can be used to understand "stabilization indices" of curves with potentially multiplicative reduction (joint with Daniele Turchetti).