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 loopscalled 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, reproving some of Neumann and Wahl'searlier results on these singularities, and showings that splice type surface singularities are Newton non-degenerate in the sense of Khovanskii.[-]

Pham and Teissier showed in the late 60's that any two plane curve germs with the same outer Lipschitz geometry have equivalent embeddings into $\mathbb{C}^2$. We consider to what extent the same holds in higher dimensions, giving examples of normal surface singularities which have the same topology and outer Lipschitz geometry but whose embeddings into $\mathbb{C}^3$ are topologically inequivalent. Joint work with Anne Pichon.

Keywords: bilipschitz - Lipschitz geometry - normal surface singularity - Zariski equisingularity - Lipschitz equisingularity[-]