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A proof of Neumann and Wahl's Milnor fibre conjecture via logarithmic geometry - lecture 3

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Authors : Popescu-Pampu, Patrick (Author of the conference)
CIRM (Publisher )

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Abstract : 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.

Keywords : surface singularities; Milnor fibres; log geometry; tropicalization

MSC Codes :
32S25 - Surface and hypersurface singularities [See also 14J17]
32S50 - Topological aspects: Lefschetz theorems, topological classification, invariants
32S55 - Milnor fibration; relations with knot theory
14T90 - Applications of tropical geometry
14A21 - Logarithmic algebraic geometry, log schemes

    Information on the Video

    Film maker : Hennenfent, Guillaume
    Language : English
    Available date : 27/09/2021
    Conference Date : 09/09/2021
    Subseries : Research School
    arXiv category : Complex Variables ; Algebraic Geometry
    Mathematical Area(s) : Algebraic & Complex Geometry
    Format : MP4 (.mp4) - HD
    Video Time : 01:02:19
    Targeted Audience : Researchers
    Download : https://videos.cirm-math.fr/2021-09-09_Popescu-Pampu_3.mp4

Information on the Event

Event Title : 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
Event Organizers : Budur, Nero ; Fernandez de Bobadilla, Javier ; Pichon, Anne
Dates : 06/09/2021 - 10/09/2021
Event Year : 2021
Event URL : https://www.chairejeanmorlet.com/2570.html

Citation Data

DOI : 10.24350/CIRM.V.19799403
Cite this video as: Popescu-Pampu, Patrick (2021). A proof of Neumann and Wahl's Milnor fibre conjecture via logarithmic geometry - lecture 3. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19799403
URI : http://dx.doi.org/10.24350/CIRM.V.19799403

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