Transcendental functions with small singular sets | Vidéo | Carmin.tv

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Transcendental functions with small singular sets

By Christopher Bishop

Appears in collection : Advancing Bridges in Complex Dynamics / Avancer les connections dans la dynamique complexe

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).

Information about the video

Date of recording 20/09/2021
Date of publication 02/11/2021
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.19810603
Cite this video Bishop, Christopher (20/09/2021). Transcendental functions with small singular sets. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19810603
URL https://dx.doi.org/10.24350/CIRM.V.19810603

Domain(s)

Dynamical Systems

Bibliography

BISHOP, Christopher J. et LAZEBNIK, Kirill. Prescribing the postsingular dynamics of meromorphic functions. Mathematische Annalen, 2019, vol. 375, no 3, p. 1761-1782. - https://doi.org/10.1007/s00208-019-01869-6
BISHOP, Christopher J. Models for the Speiser class. Proceedings of the London Mathematical Society, 2017, vol. 114, no 5, p. 765-797. - https://doi.org/10.1112/plms.12025
BISHOP, Christopher J. Models for the Eremenko–Lyubich class. Journal of the London Mathematical Society, 2015, vol. 92, no 1, p. 202-221. - https://doi.org/10.1112/jlms/jdv021
BISHOP, Christopher J. Constructing entire functions by quasiconformal folding. Acta Mathematica, 2015, vol. 214, no 1, p. 1-60. - https://doi.org/10.1007/s11511-015-0122-0
BISHOP, Christopher J. et REMPE, Lasse. Non-compact Riemann surfaces are equilaterally triangulable. arXiv preprint arXiv:2103.16702, 2021. - https://arxiv.org/pdf/2103.16702.pdf

MSC codes

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