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Tropical and logarithmic techniques for the study of Milnor fibers - Lecture 3
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Authors : ... (Author of the conference)
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14B05 - Singularities
14M25 - Toric varieties, Newton polyhedra
32S05 - Local singularities [See also 14J17]
32S55 - Milnor fibration; relations with knot theory
14T90 - Applications of tropical geometry
14A21 - Logarithmic algebraic geometry, log schemes
Additional resources :
https://www.cirm-math.fr/RepOrga/3267/Slides/2025-01-Popescu-CIRM.pdf
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Abstract :
I will explain how to combine tools of local tropical geometry and logarithmic geometry in order to study the structure of Milnor fibers of smoothings of isolated complex singularities, up to homeomorphisms. I will partly follow the paper “The Milnor fiber conjecture of Neumann and Wahl, and an overview of its proof”, written in collaboration with Marıa Angelica Cueto and Dmitry Stepanov.This course replaces a course on the same topic that should have been delivered by Angelica Cueto.
Keywords : log geometry; real oriented blow up; singularity theory, toric geometry; tropical geometry
MSC Codes : Keywords : log geometry; real oriented blow up; singularity theory, toric geometry; tropical geometry
14B05 - Singularities
14M25 - Toric varieties, Newton polyhedra
32S05 - Local singularities [See also 14J17]
32S55 - Milnor fibration; relations with knot theory
14T90 - Applications of tropical geometry
14A21 - Logarithmic algebraic geometry, log schemes
Additional resources :
https://www.cirm-math.fr/RepOrga/3267/Slides/2025-01-Popescu-CIRM.pdf
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Information on the Video
Language : EnglishAvailable date : 14/02/2025 Conference Date : 30/01/2025 Subseries : Research School arXiv category : Algebraic Geometry ; General Topology Mathematical Area(s) : Algebraic & Complex Geometry ; Topology Format : MP4 (.mp4) - HD Video Time : 01:06:47 Targeted Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2025-01-30_Popescu-Pampu_3.mp4 
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Information on the Event
Event Title : Logarithmic and non-archimedean methods in Singularity Theory - Thematic Month Week 1 / Méthodes logarithmiques et non-archimédiennes en théorie des singularités - Mois thématique semaine 1Dates : 27/01/2025 - 31/01/2025 Event Year : 2025 Event URL : https://conferences.cirm-math.fr/3267.html
Citation Data
DOI : 10.24350/CIRM.V.20294703Cite this video as: (2025). Tropical and logarithmic techniques for the study of Milnor fibers - Lecture 3. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.20294703 URI : http://dx.doi.org/10.24350/CIRM.V.20294703 |
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Bibliography
- CUETO, Maria Angelica, POPESCU-PAMPU, Patrick, et STEPANOV, Dmitry. The Milnor fiber conjecture of Neumann and Wahl, and an overview of its proof. In PAPADOPOULOS, Athanase. Essays in Geometry. 2023 p.629-710 - https://doi.org/10.4171/irma/34/28
- CUETO, Maria Angelica, POPESCU-PAMPU, Patrick, et STEPANOV, Dmitry. Local tropicalizations of splice type surface singularities. Mathematische Annalen, 2024, vol. 390, no 1, p. 811-887. - https://doi.org/10.1007/s00208-023-02755-y
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