Splice type surface singularities and their local tropicalizations

Splice type surface singularities were introduced by Neumann and Wahl as a generalization of the class of Pham–Brieskorn–Hamm complete intersections of dimension two. Their construction depends on a weighted graph with no loops called a splice diagram. In this talk, I will report on joint work with Patrick Popescu–Pampu and Dmitry Stepanov (arXiv:2108.05912) that sheds new light on these singularities via tropical methods. I will discuss how to reprove some of Neumann and Wahl's earlier results on these singularities, and show that splice type surface singularities are Newton non-degenerate in the sense of Khovanskii.