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:20260423T004701Z UID:ags/5 DESCRIPTION:Title: Thur ston maps with four postcritical points\nby Annina Iseli (UCLA) as par t of Analysis and Geometry Seminar\n\n\nAbstract\nA Thurston map is a bran ched covering map of the 2-sphere which is not a homeomorphism and for whi ch every critical point has a finite orbit under iteration of the map. Fre quently\, a Thurston map admits a description in purely combinatorial-topo logical terms. In this context it is an interesting question whether a giv en map can (in a suitable sense) be realized by a rational map with the sa me combinatorics. This question was answered by Thurston in the 1980's in his celebrated characterization of rational maps. Thurston's Theorem rough ly says that a Thurston map is realized if and only if it does not admit a Thurston obstruction\, which is an invariant multicurve that satisfies a certain growth condition. However\, in practice it can be very hard to ver ify whether a given map has no Thurston obstruction\, because\, in princip le\, one would need to check the growth condition for infinitely many curv es. \n \nIn this talk\, we will consider a specific family of Thurston map s with four postcritical points that arises from Schwarz reflections on fl apped pillows (a simple surgery of a polygonal sphere). Using a counting a rgument\, we establish a necessary and sufficient condition for a map in t his family to be realized by a rational map. In the last part of the talk\ , we will discuss a generalization of this result which states that\, give n an obstructed Thurston map with four postcritical points\, one can elimi nate obstructions by applying a so-called blowing up operation. These resu lts are joint with M. Bonk and M. Hlushchanka.\n LOCATION:https://researchseminars.org/talk/ags/5/ END:VEVENT END:VCALENDAR