By Stéphane Gaubert
On the Solutions of Knizhnik-Zamolodchikov Differential Equations by Noncommutative Picard-Vessiot Theory
By Vincel Hoang Ngoc Minh
By Paul-André Melliès
Appears in collection : Jean-Morlet Chair 2021 - Research School: Milnor Fibrations, Degenerations and Deformations from Modern Perspectives / Chaire Jean-Morlet 2021 - Ecole : Fibrations de Milnor, dégénérescences et déformations : perpectives modernes
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.