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Seminar

COMD Essential Seminar Series: Polynomial Approximations in Class S May 26, 2022 (11:00 AM PDT - 12:00 PM PDT)
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Location: MSRI: Simons Auditorium, Online/Virtual
Speaker(s) Nikolai Prochorov (Université d'Aix-Marseille I (Université de Provence))
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To participate in this seminar, please register HERE.

Transcendental entire maps from class S (also called Speiser class or maps of finite type) share several common properties with polynomials. This includes functional-theoretical aspects such as a similar structure of the singular set, as well as dynamical aspects, for example, the no-wandering-domains theorem, etc. 

In this talk, I will try to explain how we can look at maps from class S as limits of polynomial maps, and which dynamical meaning these approximations may have. I will start with speaking about one of the best known cases: considering exponential maps as limits of uncritical polynomials; I will state what it implies for parameter and dynamical planes of these functions. Further, I will provide a few more general results and, finally, will speak about how we hope to construct "dynamically meaningful" polynomial approximations for arbitrary maps in class S using planar embedded graphs. This is joint work with Malavika Mukundan and Bernhard Reinke.

 

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