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The non-archimedean SYZ fibration and Igusa zeta functions - Part 1
Post-edited
Authors : Nicaise, Johannes (Author of the conference)
CIRM (Publisher )
14B05 - Singularities
14D06 - Fibrations, degenerations
14E30 - Minimal model program (Mori theory, extremal rays)
14G10 - Zeta-functions and related questions
14G22 - Rigid analytic geometry
14E18 - Arcs and motivic integration
CIRM (Publisher )
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| string theory: mirror symmetry SYZ fibration Berkovich spaces monomial points |
Abstract :
The SYZ fibration is a conjectural geometric explanation for the phenomenon of mirror symmetry for maximal degenerations of complex Calabi-Yau varieties. I will explain Kontsevich and Soibelman's construction of the SYZ fibration in the world of non-archimedean geometry, and its relations with the Minimal Model Program and Igusa's p-adic zeta functions. No prior knowledge of non-archimedean geometry is assumed. These lectures are based on joint work with Mircea Mustata and Chenyang Xu.
MSC Codes : 14B05 - Singularities
14D06 - Fibrations, degenerations
14E30 - Minimal model program (Mori theory, extremal rays)
14G10 - Zeta-functions and related questions
14G22 - Rigid analytic geometry
14E18 - Arcs and motivic integration
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 20/09/2016 Conference Date : 13/09/2016 Subseries : Research talks arXiv category : Algebraic Geometry Mathematical Area(s) : Algebraic & Complex Geometry Format : MP4 (.mp4) - HD Video Time : 00:51:43 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2016-09-14_Nicaise_part1.mp4 
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Information on the Event
Event Title : Higher dimensional algebraic geometry and characteristic p > 0 / Géométrie algébrique en dimension supérieure et caractéristique p > 0Event Organizers : Blickle, Manuel ; Schwede, Karl ; Xu, Chenyang Dates : 12/09/2016 - 16/09/2016 Event Year : 2016 Event URL : http://conferences.cirm-math.fr/1376.html
Citation Data
DOI : 10.24350/CIRM.V.19048503Cite this video as: Nicaise, Johannes (2016). The non-archimedean SYZ fibration and Igusa zeta functions - Part 1. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19048503 URI : http://dx.doi.org/10.24350/CIRM.V.19048503 |
See Also
- [Multi angle] Fourier-Mukai partners of canonical covers in positive characteristic / Author of the conference Tirabassi, Sofia.
- [Multi angle] Crystalline cohomology, period maps, and applications to K3 surfaces / Author of the conference Liedtke, Christian.
- [Multi angle] The non-archimedean SYZ fibration and Igusa zeta functions - Part 3 / Author of the conference Nicaise, Johannes.
- [Multi angle] The non-archimedean SYZ fibration and Igusa zeta functions - Part 2 / Author of the conference Nicaise, Johannes.
Bibliography
- Mustata, M., & Nicaise, J. (2015). Weight functions on non-Archimedean analytic spaces and the Kontsevich-Soibelman skeleton. Algebraic Geometry, 2(3), 365-404 - http://dx.doi.org/10.14231/AG-2015-016
- Nicaise, J., & Xu, C. (2016). Poles of maximal order of motivic zeta functions. Duke Mathematical Journal, 165(2), 217-243 - http://dx.doi.org/10.1215/00127094-3165648
- Nicaise, J., & Xu, C. (2016). The essential skeleton of a degeneration of algebraic varieties.
- Nicaise, J. (2016). Berkovich skeleta and birational geometry. In M. Baker, & S. Payne (Eds.), Nonarchimedean and Tropical Geometry (pp. 173-194). Berlin: Springer - http://dx.doi.org/10.1007/978-3-319-30945-3_7
