Dynamical Systems and Analysis Seminar - Lasse Rempe
| Dates: | 30 September 2024 |
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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: Lasse Rempe (University of Manchester)
Title: A counterexample to Eremenko's conjecture
Abstract: Let f be an entire function (i.e., a holomorphic self-map of the complex plane), and suppose that f is transcendental, i.e., not a polynomial. The *escaping set* of f consists of those points that tend to infinity under repeated application of f. (For example, all real numbers belong to the escaping set of the exponential map, since they tend to infinity under repeated exponentiation.) In 1989, Eremenko conjectured that every connected component of the escaping set is unbounded.
Eremenko's conjecture has been a central problem in transcendental dynamics in the past decade. A number of stronger versions of the conjecture have been disproved, while weaker ones has been established, and the conjecture has also been shown to hold for a number of classes of functions. I will describe recent work with David MartÃ-Pete and James Waterman in which we construct a counterexample to the conjecture. The talk should be accessible to a general mathematical audience, including PhD students.
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
