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SUMMARY:Junior Geometry Seminar –  Carmine Imbriani (Milan)
DESCRIPTION:Title: The Holonomy Representation of Projective Structures on 
 Compact Riemann Surfaces\nSpeaker: Carmine Imbriani\n\n\n\n\n\n\nAbstract:
  Complex projective structures provide a compelling example of (G\,X)-stru
 ctures on surfaces\, serving as a bridge between classical uniformization 
 theory and modern representation theory. This seminar explores the geometr
 ic and algebraic properties of these structures\, with a primary focus on 
 the holonomy map hol from the space of projective structures P(S) to th
 e PSL(2\, C)-character variety of the fundamental group \\pi_1(S).\nWhile 
 the holonomy map is a general construction that is always open\, its behav
 ior in the context of projective structures is particularly rich: it is kn
 own to be a local homeomorphism but\, notably\, it fails to be globally in
 jective due to phenomena such as grafting. In the final part of the talk\,
  we will discuss a landmark result by R.C. Gunning\, which provides a crit
 erion for the injectivity of the holonomy map. By restricting the domain t
 o a special class of projective structures\, we will show how it is possib
 le to recover a unique correspondence between projective structures and th
 eir associated representations.\n\n\n\n\n\n\n\n \n\n\n\n\nSome snacks wil
 l be provided before and after the talk.\nGo to the seminar main page.\nSu
 bscribe to the mailing list.\n
URL:https://www.imperial.ac.uk/events/209446/junior-geometry-seminar-carmin
 e-imbriani/
DTSTART;TZID=Europe/London:20260515T173000
DTEND;TZID=Europe/London:20260515T183000
LOCATION:Room 140\, Huxley Building\, South Kensington Campus\, Imperial Co
 llege London\, London\, SW7 2AZ\, United Kingdom
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