BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Lukas Geyer (Montana State University) DTSTART:20200922T130000Z DTEND:20200922T140000Z DTSTAMP:20260422T201504Z UID:CAvid/13 DESCRIPTION:Title: G ravitational lensing and critically fixed anti-rational maps\nby Lukas Geyer (Montana State University) as part of CAvid: Complex Analysis video seminar\n\nLecture held in N/A.\n\nAbstract\nStudying the dynamics of ant i-rational maps\, i.e.\, complex conjugates of rational maps\, is a subjec t closely related to holomorphic dynamics\, with intriguing connections to problems in gravitational lensing. In particular\, the lens equation for a single-plane gravitational lens made up of N point masses is known to be a fixed point equation for an anti-rational map of degree N. These fixed points are apparent images of a single (point) light source\, and it is kn own from work of Rhie (2003) and Khavinson and Neumann (2006) that for N>1 there can be at most 5N-5 such images\, and that this bound is sharp.\n\n Originally motivated by the goal of classifying maximal lensing configurat ions\, i.e.\, configurations for which the bound 5N-5 is attained\, we rec ently succeeded in giving a complete classification of anti-rational maps for which all critical points are fixed\, through simple topological model s associated with certain planar graphs. We will explain this classificati on\, the main ideas in the proof\, and how this yields a partial classific ation and new examples of maximal lensing configurations. Finally\, we wil l discuss some open problems and questions.\n LOCATION:https://researchseminars.org/talk/CAvid/13/ END:VEVENT END:VCALENDAR