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Tropical and logarithmic techniques for the study of Milnor fibers - lecture 2
Multi angle
Authors : Popescu-Pampu, Patrick (Author of the conference)
CIRM (Publisher )
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
CIRM (Publisher )
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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
Film maker : Recanzone, LucaLanguage : English Available date : 14/02/2025 Conference Date : 29/01/2025 Subseries : Research School arXiv category : Algebraic Geometry ; Geometric Topology Mathematical Area(s) : Algebraic & Complex Geometry ; Topology Format : MP4 (.mp4) - HD Video Time : 01:03:01 Targeted Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2025-01-29_Popescu_Pampu_2.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 1Event Organizers : Fantini, Lorenzo ; Pełka, Tomasz ; Pichon, Anne ; Rond, Guillaume Dates : 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.20294603Cite this video as: Popescu-Pampu, Patrick (2025). Tropical and logarithmic techniques for the study of Milnor fibers - lecture 2. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.20294603 URI : http://dx.doi.org/10.24350/CIRM.V.20294603 |
See Also
- [Multi angle] Resolution of foliated varieties by torus actions / Author of the conference Wlodarczyk , Jaroslaw.
- [Multi angle] Semialgebraic Whitney partition of unity / Author of the conference Valette, Anna.
- [Multi angle] Semi-homogeneous bundles, Fourier-Mukai transforms, and tropicalization / Author of the conference Ulirsch, Martin.
- [Multi angle] Tropical and logarithmic techniques for the study of Milnor fibers - Lecture 3 / Author of the conference Popescu-Pampu, Patrick.
- [Multi angle] Tropical and logarithmic techniques for the study of Milnor fibers - Lecture 1 / Author of the conference Popescu-Pampu, Patrick.
- [Multi angle] Specialization techniques and stable rationality - Lecture 3 / Author of the conference Ottem, John Christian.
- [Multi angle] Specialization techniques and stable rationality - Lecture 2 - the motivic volume formula of Nicaise-Shinder / Author of the conference Ottem, John Christian.
- [Multi angle] Specialization techniques and stable rationality - Lecture 1 / Author of the conference Ottem, John Christian.
- [Multi angle] Piecewise linear geometry and spaces of valuations / Author of the conference Loeser, François.
- [Multi angle] A universal motivic invariant of birational maps / Author of the conference Lin, Hsueh-Yung.
- [Multi angle] Nash blowup fails to resolve singularities in dimensions four and higher / Author of the conference Leyton-Álvarez, Maximiliano.
- [Multi angle] A singular path through toric geometry / Author of the conference Gonzalez Perez, Pedro Daniel.
- [Multi angle] Teissier singularities / Author of the conference Mourtada, Hussein.
- [Multi angle] Motivic invariants via non-archimedean geometry - Lecture 3 / Author of the conference Forey, Arthur.
- [Multi angle] Motivic invariants via non-archimedean geometry - Lecture 2 / Author of the conference Forey, Arthur.
- [Multi angle] Motivic invariants via non-archimedean geometry - Lecture 1 / Author of the conference Forey, Arthur.
- [Multi angle] Motivic Milnor fibre and logarithmic geometry / Author of the conference Fichou, Goulwen.
- [Multi angle] Generic theta divisors / Author of the conference Budur, Nero.
- [Multi angle] The KSBA moduli space of stable log Calabi-Yau surfaces / Author of the conference Argüz, Hülya.
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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