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Number theory through geometry, dynamics and illustration - Lecture 2
Multi angle
Authors : Stange, Katherine (Author of the conference)
CIRM (Publisher )
11J70 - Continued fractions and generalizations
11J99 - None of the above but in this section
37F32 - Fuchsian and Kleinian groups as dynamical systems
CIRM (Publisher )
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Abstract :
The course will explore several related topics in number theory with dynamical and/or geometric facets: continued fractions, Diophantine approximation, and Apollonian circle packings. We will focus on both theoretical and experimental tools, a parallel goal will be to experience the role of visualization and illustration in mathematical research. In covering background material, the approach will emphasize the visual and dynamical:
(1) Continued fractions, quadratic forms, and Diophantine approximation.
(2) Hyperbolic geometry, Minkowski space, and Kleinian groups.
With these tools at hand, we will study some areas of current research:
(1) The geometry of Diophantine approximation and continued fractions in the complex plane,including algebraic starscapes and Schmidt arrangements.
(2) Apollonian circle packings, with an emphasis on their surprising relationships to the preceding topics.
Keywords : continued fractions; Apollonian circle packings; Diophantine approximation; Kleinian groups
MSC Codes : (1) Continued fractions, quadratic forms, and Diophantine approximation.
(2) Hyperbolic geometry, Minkowski space, and Kleinian groups.
With these tools at hand, we will study some areas of current research:
(1) The geometry of Diophantine approximation and continued fractions in the complex plane,including algebraic starscapes and Schmidt arrangements.
(2) Apollonian circle packings, with an emphasis on their surprising relationships to the preceding topics.
Keywords : continued fractions; Apollonian circle packings; Diophantine approximation; Kleinian groups
11J70 - Continued fractions and generalizations
11J99 - None of the above but in this section
37F32 - Fuchsian and Kleinian groups as dynamical systems
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Information on the Video
Film maker : Recanzone, LucaLanguage : English Available date : 25/07/2023 Conference Date : 11/07/2023 Subseries : Research School arXiv category : Number Theory Mathematical Area(s) : Number Theory Format : MP4 (.mp4) - HD Video Time : 00:54:19 Targeted Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2023-07-11_Stange_1.mp4 
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Information on the Event
Event Title : Jean Morlet Chair - School -Renormalization and Visualization for packing, Billiard and Surfaces / Chaire Jean-Morlet - Ecole - Renormalisation et visualisation pour des problèmes d'empilement, de billard et de surfacesEvent Organizers : Athreya, Jayadev ; Bedaride, Nicolas Dates : 10/07/2023 - 14/07/2023 Event Year : 2023 Event URL : https://conferences.cirm-math.fr/2794.html
Citation Data
DOI : 10.24350/CIRM.V.20070603Cite this video as: Stange, Katherine (2023). Number theory through geometry, dynamics and illustration - Lecture 2. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.20070603 URI : http://dx.doi.org/10.24350/CIRM.V.20070603 |
See Also
- [Multi angle] Number theory through geometry, dynamics and illustration - Lecture 3 / Author of the conference Stange, Katherine.
- [Multi angle] Number theory through geometry, dynamics and illustration - Lecture 1 / Author of the conference Stange, Katherine.
- [Multi angle] Billiard, outer billiard, simplectic billiard, programs: Mc billiard, billiard king. / Author of the conference Schwartz, Richard-Evan.
- [Multi angle] Renormalization: Masur and Veech solution to Keane conjecture. Moreira-Yoccoz solution to Palis conjecture / Author of the conference Matheus, Carlos.
Bibliography
