Dynamical Systems and Analysis Seminar - Nikolai Prochorov
| Dates: | 10 November 2025 |
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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: Nikolai Prochorov (Institut de Mathématiques de Marseille)
Title: Thurston theory for critically fixed branched covering maps
Abstract: In the 1980’s, William Thurston obtained his celebrated characterization of rational mappings. This result laid the foundation of such a field as Thurston's theory of holomorphic maps, which has been actively developing in the last few decades. One of the most important problems in this area is the questions about characterization, which is understanding when a topological map is equivalent (in a certain dynamical sense) to a holomorphic one, and classification, which is an enumeration of all possible topological models of holomorphic maps from a given class.
In my talk, I am going to focus on the characterization and classification problems for the family of critically fixed branched coverings, i.e., branched coverings of the 2-dimensional sphere S^2 with all critical points being fixed. Maps of this family can be defined by combinatorial models based on planar embedded graphs, and it provides an elegant answer to the classification problem for this family. Further, I plan to explain how to understand whether a given critically fixed branched cover is equivalent to a critically fixed rational map of the Riemann sphere and provide an algorithm of combinatorial nature that allows us to answer this question. This is a joint work with Mikhail Hlushchanka.
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
