BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Nikolai Prochorov (Marseille) DTSTART:20240425T130500Z DTEND:20240425T140000Z DTSTAMP:20260423T021102Z UID:GaTO/101 DESCRIPTION:Title: T hurston theory for critically fixed branched covering maps\nby Nikolai Prochorov (Marseille) as part of Geometry and topology online\n\nLecture held in Room B3.02 in the Zeeman Building\, University of Warwick.\n\nAbst ract\nIn the 1980’s\, William Thurston obtained his celebrated character isation of rational mappings. This result laid the foundation of such a fi eld as Thurston's theory of holomorphic maps\, which has been actively dev eloping in the last few decades. One of the most important problems in thi s area is the questions about characterisation\, which is understanding wh en a topological map is equivalent (in a certain dynamical sense) to a hol omorphic one\, and classification\, which is an enumeration of all possibl e topological models of holomorphic maps from a given class.\n\nIn my talk \, I am going to focus on the characterisation and classification problems for the family of post-critically finite branched coverings\, i.e.\, bran ched coverings of the two-dimensional sphere $S^2$ with all critical point s 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 t o understand whether a given critically fixed branched cover is equivalent to a critically fixed rational map of the Riemann sphere and provide an a lgorithm of combinatorial nature that allows us to answer this question. F inally\, if time permits\, I will briefly mention the connections between Thurston's theory\, Teichmüller spaces and Mapping Class Groups of marked spheres.\n\nThis is a joint work with Mikhail Hlushchanka.\n LOCATION:https://researchseminars.org/talk/GaTO/101/ END:VEVENT END:VCALENDAR