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Complexity theory in arithmetic dynamical systems - Lecture 1
Virtualconference
Authors : Xie, Junyi (Author of the conference)
CIRM (Publisher )
11-XX - Number theory
14-XX - Algebraic geometry
37-XX - dynamical system - ergodic theory
CIRM (Publisher )
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Abstract :
It is a fundamental problem to measure the complexity of a dynamical system. In this lecture, we discuss this problem for arithmetic dynamics in terms of topology, algebra and arithmetic. In particular, the notion of dynamical degrees, which can be viewed as an algebraic analogy of “entropy”, plays a key role. We will see how it applies to study the orbits, periodic points and action of cohomologies.
MSC Codes : 11-XX - Number theory
14-XX - Algebraic geometry
37-XX - dynamical system - ergodic theory
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Information on the Video
Film maker : Recanzone, LucaLanguage : English Available date : 10/02/2025 Conference Date : 23/01/2025 Subseries : Research School arXiv category : Algebraic Geometry ; Algebraic Topology Mathematical Area(s) : Algebraic & Complex Geometry Format : MP4 (.mp4) - HD Video Time : 01:27:44 Targeted Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2025-01-23_Xie_1.mp4 
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Information on the Event
Event Title : Etats de la recherche: Arithmetic, Algebraic and Analytics Dynamics / Etats de la recherche: Dynamique arithmétique, algébrique, et analytiqueEvent Organizers : Favre, Charles ; Gauthier, Thomas ; Raissy, Jasmin Dates : 20/01/2025 - 24/01/2025 Event Year : 2025 Event URL : https://conferences.cirm-math.fr/3211.html
Citation Data
DOI : 10.24350/CIRM.V.20290503Cite this video as: Xie, Junyi (2025). Complexity theory in arithmetic dynamical systems - Lecture 1. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.20290503 URI : http://dx.doi.org/10.24350/CIRM.V.20290503 |
See Also
- [Virtualconference] Complexity theory in arithmetic dynamical systems - Lecture 3 / Author of the conference Xie, Junyi.
- [Virtualconference] Complexity theory in arithmetic dynamical systems - Lecture 2 / Author of the conference Xie, Junyi.
- [Multi angle] Degeneration of rational maps and hyperbolic components Lecture 3 / Author of the conference Luo, Yusheng.
- [Multi angle] Degeneration of rational maps and hyperbolic components - Lecture 2 / Author of the conference Luo, Yusheng.
- [Multi angle] The group of tame automorphisms - Lecture 3 / Author of the conference Lamy, Stéphane.
- [Multi angle] the group of tame automorphisms - Lecture 2 / Author of the conference Lamy, Stéphane.
- [Multi angle] Geometry and algebra of preperiodic points in $ \mathbb{P}^{N}$ - Lecture 3 / Author of the conference Demarco, Laura.
- [Multi angle] Geometry and algebra of preperiodic points in $ \mathbb{P}^{N}$ - Lecture 2 / Author of the conference Demarco, Laura.
- [Multi angle] Degeneration of rational maps and hyperbolic components - Lecture 1 / Author of the conference Luo, Yusheng.
- [Multi angle] the group of tame automorphisms - Lecture 1 / Author of the conference Lamy, Stéphane.
- [Multi angle] Geometry and algebra of preperiodic points in $ \mathbb{P}^{N}$ - Lecture 1 / Author of the conference Demarco, Laura.
- [Multi angle] Intersection theory and heights : birational perspective / Author of the conference Chambert-Loir, Antoine.
- [Multi angle] Rigidity and examples / Author of the conference Cantat, Serge.
Bibliography
