Pure Maths Colloquium - Commuting functions and wandering domains - Gwyneth Stallard (Open U) Seminar
- Time:
- 15:00 - 16:00
- Date:
- 10 March 2017
- Venue:
- Lecture Theatre 10B, Room 10037, Mathematical Sciences, Building 54, University of Southampton, Highfield, Southampton, SO17 1BJ
For more information regarding this seminar, please telephone Dr Jan Spakula on 023 8059 3137 or email Jan.Spakula@southampton.ac.uk .
Event details
Abstract: A basic question in complex analysis is, given an analytic function, can you determine which other analytic functions it commutes with? Although this question was solved for rational functions around 100 years ago, it remains open in general. A key step in solving this question is to determine whether, if two analytic functions commute, are their Julia sets equal? (The Julia set of a function is the set of points that behave chaotically under iteration.) In this talk we describe how a new understanding of wandering domains of analytic functions has enabled us to make progress on this problem. This is joint work with Anna Benini and Phil Rippon
Speaker information
Professor Gwyneth Stallard , The Open University. My research is in the area of complex dynamics and concerns the iteration of transcendental meromorphic functions. I am particularly interested in the possible dimensions of the Julia set and in the structure of the escaping set. Together with Professor Phil Rippon, I lead the complex dynamics group at the OU. The group currently comprises a Visiting Research Associate and two PhD students and our activities often include other complex analysts in the department. Phil Rippon and myself are currently working on a project to investigate a surprising link that we identified between two open conjectures in complex dynamics: Baker's conjecture and Eremenko's conjecture. The work has been funded by the EPSRC by two grants which together funded our work for five years (0.5FTE each).