English
Tropical and logarithmic techniques for the study of Milnor fibers - Lecture 3
Multi angle
Auteurs : Popescu-Pampu, Patrick (Auteur de la Conférence)
CIRM (Editeur )
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
Ressources complémentaires :
https://www.cirm-math.fr/RepOrga/3267/Slides/2025-01-Popescu-CIRM.pdf
CIRM (Editeur )
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Résumé :
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
Codes MSC : 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
Ressources complémentaires :
https://www.cirm-math.fr/RepOrga/3267/Slides/2025-01-Popescu-CIRM.pdf
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Informations sur la Vidéo
Réalisateur : Recanzone, LucaLangue : Anglais Date de publication : 14/02/2025 Date de captation : 30/01/2025 Sous collection : Research School arXiv category : Algebraic Geometry ; General Topology Domaine : Algebraic & Complex Geometry ; Topology Format : MP4 (.mp4) - HD Durée : 01:06:47 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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Informations sur la Rencontre
Nom de la rencontre : Logarithmic and non-archimedean methods in Singularity Theory - Thematic Month Week 1 / Méthodes logarithmiques et non-archimédiennes en théorie des singularités - Mois thématique semaine 1Organisateurs de la rencontre : Fantini, Lorenzo ; Pełka, Tomasz ; Pichon, Anne ; Rond, Guillaume Dates : 27/01/2025 - 31/01/2025 Année de la rencontre : 2025 URL Congrès : https://conferences.cirm-math.fr/3267.html
Données de citation
DOI : 10.24350/CIRM.V.20294703Citer cette vidéo: Popescu-Pampu, Patrick (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 |
Voir aussi
- [Multi angle] Resolution of foliated varieties by torus actions / Auteur de la Conférence Wlodarczyk , Jaroslaw.
- [Multi angle] Semialgebraic Whitney partition of unity / Auteur de la Conférence Valette, Anna.
- [Multi angle] Semi-homogeneous bundles, Fourier-Mukai transforms, and tropicalization / Auteur de la Conférence Ulirsch, Martin.
- [Multi angle] Tropical and logarithmic techniques for the study of Milnor fibers - lecture 2 / Auteur de la Conférence Popescu-Pampu, Patrick.
- [Multi angle] Tropical and logarithmic techniques for the study of Milnor fibers - Lecture 1 / Auteur de la Conférence Popescu-Pampu, Patrick.
- [Multi angle] Specialization techniques and stable rationality - Lecture 3 / Auteur de la Conférence Ottem, John Christian.
- [Multi angle] Specialization techniques and stable rationality - Lecture 2 - the motivic volume formula of Nicaise-Shinder / Auteur de la Conférence Ottem, John Christian.
- [Multi angle] Specialization techniques and stable rationality - Lecture 1 / Auteur de la Conférence Ottem, John Christian.
- [Multi angle] Piecewise linear geometry and spaces of valuations / Auteur de la Conférence Loeser, François.
- [Multi angle] A universal motivic invariant of birational maps / Auteur de la Conférence Lin, Hsueh-Yung.
- [Multi angle] Nash blowup fails to resolve singularities in dimensions four and higher / Auteur de la Conférence Leyton-Álvarez, Maximiliano.
- [Multi angle] A singular path through toric geometry / Auteur de la Conférence Gonzalez Perez, Pedro Daniel.
- [Multi angle] Teissier singularities / Auteur de la Conférence Mourtada, Hussein.
- [Multi angle] Motivic invariants via non-archimedean geometry - Lecture 3 / Auteur de la Conférence Forey, Arthur.
- [Multi angle] Motivic invariants via non-archimedean geometry - Lecture 2 / Auteur de la Conférence Forey, Arthur.
- [Multi angle] Motivic invariants via non-archimedean geometry - Lecture 1 / Auteur de la Conférence Forey, Arthur.
- [Multi angle] Motivic Milnor fibre and logarithmic geometry / Auteur de la Conférence Fichou, Goulwen.
- [Multi angle] Generic theta divisors / Auteur de la Conférence Budur, Nero.
- [Multi angle] The KSBA moduli space of stable log Calabi-Yau surfaces / Auteur de la Conférence Argüz, Hülya.
- [Multi angle] $D$-modules and $p$-curvatures / Auteur de la Conférence Esnault, Hélène.
Bibliographie
- 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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