Dynamical Systems and Analysis Seminar - Julia Münch
| Dates: | 2 February 2026 |
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| Times: | 14:00 - 15:00 |
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| What is it: | Seminar |
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| Organiser: | Department of Mathematics |
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| Who is it for: | University staff, External researchers, Current University students |
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Speaker: Julia Münch (University of Liverpool)
Title: Extensions and applications to Sullivan's dictionary
Abstract: For generalising complex dynamics to higher real dimensions it is natural to consider quasi-regular mappings. The subfamily of uniformly quasi-regular mappings is particularly well understood but it is difficult to find interesting examples. I will be talking about a result obtained joint with Daniel Meyer; we showed that one can extend a certain class of holomorphic functions (expanding Thurston maps) on the Riemann sphere S^2 to a uniformly quasi-regular mapping F defined on a subset ? of R^3 containing S^2 in its interior.
In the second part of the talk we will present two applications of this construction that is motivated by Sullivan’s dictionary. Sullivan’s dictionary stipulates an analogy between objects, conjectures and theorems in complex dynamics and the study of Kleinian groups. We will examine the properties of the extension F with respect to the hyperbolic metric, and show an application that has a counterpart in the theory of Kleinian groups. The aim of the talk is to explain a construction of a space-filling curve that is the boundary of an immersed and severely folded plane.
Room: Frank Adams 1
Further information: https://personalpages.manchester.ac.uk/staff/yotam.smilansky/dynamics_analysis
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Frank Adams 1
Alan Turing Building
Manchester
