The splice type singularities introduced in 2001 by Neumann and Wahl provide the largest class known so far of links of isolated complete intersection surface singularities which are integral homology spheres. These singularities are determined up to equisingularity by particular kinds of decorated trees, called splice diagrams. Neumann and Wahl formulated the so-called Milnor fiber conjecture, stating that any choice of an internal edge of a splice diagram determines a kind of four-dimensional decomposition of the Milnor fiber of the associated singularity. The aim of this course is to explain the structure of a proof of this conjecture, obtained in collaboration with Maria Angelica Cueto and Dmitry Stepanov. lt uses a combination of toric, tropical and logarithmic geometry. [-]

The splice type singularities introduced in 2001 by Neumann and Wahl provide the largest class known so far of links of isolated complete intersection surface singularities which are integral homology spheres. These singularities are determined up to equisingularity by particular kinds of decorated trees, called splice diagrams. Neumann and Wahl formulated the so-called Milnor fiber conjecture, stating that any choice of an internal edge of a splice diagram determines a kind of four-dimensional decomposition of the Milnor fiber of the associated singularity. The aim of this course is to explain the structure of a proof of this conjecture, obtained in collaboration with Maria Angelica Cueto and Dmitry Stepanov. lt uses a combination of toric, tropical and logarithmic geometry. [-]

The splice type singularities introduced in 2001 by Neumann and Wahl provide the largest class known so far of links of isolated complete intersection surface singularities which are integral homology spheres. These singularities are determined up to equisingularity by particular kinds of decorated trees, called splice diagrams. Neumann and Wahl formulated the so-called Milnor fiber conjecture, stating that any choice of an internal edge of a splice diagram determines a kind of four-dimensional decomposition of the Milnor fiber of the associated singularity. The aim of this course is to explain the structure of a proof of this conjecture, obtained in collaboration with Maria Angelica Cueto and Dmitry Stepanov. lt uses a combination of toric, tropical and logarithmic geometry. [-]

The splice type singularities introduced in 2001 by Neumann and Wahl provide the largest class known so far of links of isolated complete intersection surface singularities which are integral homology spheres. These singularities are determined up to equisingularity by particular kinds of decorated trees, called splice diagrams. Neumann and Wahl formulated the so-called Milnor fiber conjecture, stating that any choice of an internal edge of a splice diagram determines a kind of four-dimensional decomposition of the Milnor fiber of the associated singularity. The aim of this course is to explain the structure of a proof of this conjecture, obtained in collaboration with Maria Angelica Cueto and Dmitry Stepanov. lt uses a combination of toric, tropical and logarithmic geometry. [-]

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.[-]