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Transcendental functions with small singular sets

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Virtualconference
Authors : Bishop, Christopher (Author of the conference)
CIRM (Publisher )

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Abstract : I will introduce the Speiser and Eremenko-Lyubich classes of transcendental entire functions and give a brief review of quasiconformal maps and the measurable Riemann mapping theorem. I will then discuss tracts and models for the Eremenko-Lyubich class and state the theorem that all topological tracts can occur in this class. A more limited result for the Speiser class will also be given. I will then discuss some applications of these ideas, focusing on recent work with Kirill Lazebnik (prescribing postsingular orbits of meromorphic functions) and Lasse Rempe (equilateral triangulations of Riemann surfaces).

Keywords : Transcendental dynamics; quasiconformal folding; postsingular set; Riemann surfaces

MSC Codes :
30D20 - Entire functions, general theory
30F99 - None of the above but in this section
37F10 - Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets

    Information on the Video

    Film maker : Hennenfent, Guillaume
    Language : English
    Available date : 02/11/2021
    Conference Date : 20/09/2021
    Subseries : Research School
    arXiv category : Dynamical Systems
    Mathematical Area(s) : Analysis and its Applications ; Dynamical Systems & ODE
    Format : MP4 (.mp4) - HD
    Video Time : 01:05:21
    Targeted Audience : Researchers
    Download : https://videos.cirm-math.fr/2021-09-20_Bishop.mp4

Information on the Event

Event Title : Advancing Bridges in Complex Dynamics / Avancer les connections dans la dynamique complexe
Event Organizers : Benini, Anna Miriam ; Drach, Kostiantyn ; Dudko, Dzmitry ; Hlushchanka, Mikhail ; Schleicher, Dierk
Dates : 20/09/2021 - 24/09/2021
Event Year : 2021
Event URL : https://conferences.cirm-math.fr/2546.html

Citation Data

DOI : 10.24350/CIRM.V.19810603
Cite this video as: Bishop, Christopher (2021). Transcendental functions with small singular sets. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19810603
URI : http://dx.doi.org/10.24350/CIRM.V.19810603

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