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Number theory through geometry, dynamics and illustration - Lecture 3

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Authors : Stange, Katherine (Author of the conference)
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 :
11J70 - Continued fractions and generalizations
11J99 - None of the above but in this section
37F32 - Fuchsian and Kleinian groups as dynamical systems

    Information on the Video

    Film maker : Recanzone, Luca
    Language : English
    Available date : 25/07/2023
    Conference Date : 13/07/2023
    Subseries : Research School
    arXiv category : Number Theory
    Mathematical Area(s) : Number Theory
    Format : MP4 (.mp4) - HD
    Video Time : 01:05:35
    Targeted Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students
    Download : https://videos.cirm-math.fr/2023-07-13_Stange_1.mp4

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 surfaces
Event 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.20070703
Cite this video as: Stange, Katherine (2023). Number theory through geometry, dynamics and illustration - Lecture 3. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.20070703
URI : http://dx.doi.org/10.24350/CIRM.V.20070703

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