Andrew Obus

Fun with Mac Lane valuations

Mac Lane's technique of "inductive valuations" is over 80 years old, but has only recently been used to attack problems about arithmetic surfaces. We will give an explicit, hands-on introduction to the theory, requiring little background beyond the definition of a non-archimedean valuation.

We will then outline how this theory is useful for resolving "weak wild" quotient singularities of arithmetic surfaces (joint with Stefan Wewers), proving conductor-discriminant inequalities for hyperelliptic and superelliptic curves (joint with Padmavathi Srinivasan), and understanding regular models of potentially Mumford curves (joint with Daniele Turchetti).