Julia Munch (University of Liverpolol)
will speak on
Title: Extending rational expanding Thurston maps
Time: 3:00PM
Date: Tue 7th April 2026
Location: E0.32 (beside Pi restaurant)
[map]
Further informationAbstract: In this talk I will present an extension result. We showed that one can extend rational expanding Thurston maps on the Riemann sphere to uniformly quasi-regular mappings of R^3. There are two main motivations, one comes from the theory of quasi-conformal mappings and one comes from generalising complex dynamics.
Quasi-conformal mappings occur naturally in many areas of analysis, however the notion is not preserved under products and it is not easy to extend a given quasi-conformal map f:R^n → R^n to a quasi-conformal map F: R^(n+1) → R^(n+1). Our result can be put in that context, but we start with a map that is not assumed to be injective.
The second motivation is to generalise holomorphic dynamics to higher dimensions. Quasi-regular mappings on R^n are a natural generalisation of holomorphic maps in C. The dynamics is particularly nice if the same eccentricity bound on ellipses holds for all iterates of the map, i.e., if we restrict to uniformly quasi-regular mappings, but it is difficult to find interesting examples of such maps.
https://ucd-ie.zoom.us/j/66800111856
(This talk is part of the Analysis series.)
PDF notice
Return to all seminars