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SUMMARY:Polynomial Pick forms for affine spheres\, real projective polygon
 s\, and surface group representations in PSL(3\,R). - Wolf\, M (Rice Unive
 rsity)
DTSTART:20150731T080000Z
DTEND:20150731T090000Z
UID:TALK60254@talks.cam.ac.uk
CONTACT:42080
DESCRIPTION:Abstract: (Joint work with David Dumas.) Discrete surface grou
 p representations into PSL(3\, R) correspond geometrically to convex real 
 projective structures on surfaces\; in turn\, these may be studied by cons
 idering the affine spheres (an interpretation of the Hitchin system of equ
 ations in this case) which project to the convex hull of their universal c
 overs. As a sequence of convex projective structures leaves all compacta i
 n its deformation space\, a subclass of the limits is described by polynom
 ial cubic differentials on affine spheres which are conformally the comple
 x plane.  We show that those particular affine spheres project to polygons
 \; along the way\, a strong estimate on asymptotics is found\, which trans
 lates to a version of Stokes data. We begin by describing the basic object
 s and context and conclude with a sketc\nh of some of the useful technique
  and an application. \n
LOCATION:Seminar Room 1\, Newton Institute
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