BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Annina Iseli (UCLA) DTSTART:20210416T220000Z DTEND:20210416T230000Z DTSTAMP:20260404T132229Z UID:ags/5 DESCRIPTION:Title: Thurston maps with four postcritical points\nby Annina Iseli (UCLA) as part of Analysis and Geometry Seminar\n\n\nAbstract\nA Thurston map is a branched covering map of the 2-sphere which is not a homeomorphism and for which every critical point has a finite orbit under iteration of the m ap. Frequently\, a Thurston map admits a description in purely combinatori al-topological terms. In this context it is an interesting question whethe r a given map can (in a suitable sense) be realized by a rational map with the same combinatorics. This question was answered by Thurston in the 198 0's in his celebrated characterization of rational maps. Thurston's Theore m roughly says that a Thurston map is realized if and only if it does not admit a Thurston obstruction\, which is an invariant multicurve that satis fies a certain growth condition. However\, in practice it can be very hard to verify whether a given map has no Thurston obstruction\, because\, in principle\, one would need to check the growth condition for infinitely ma ny curves. \n \nIn this talk\, we will consider a specific family of Thurs ton maps with four postcritical points that arises from Schwarz reflection s on flapped pillows (a simple surgery of a polygonal sphere). Using a cou nting argument\, we establish a necessary and sufficient condition for a m ap in this family to be realized by a rational map. In the last part of th e talk\, we will discuss a generalization of this result which states that \, given an obstructed Thurston map with four postcritical points\, one ca n eliminate obstructions by applying a so-called blowing up operation. The se results are joint with M. Bonk and M. Hlushchanka.\n LOCATION:https://stable.researchseminars.org/talk/ags/5/ END:VEVENT END:VCALENDAR