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SUMMARY:Emmanuel Breuillard (Oxford)
DTSTART:20220426T130000Z
DTEND:20220426T150000Z
DTSTAMP:20260423T041010Z
UID:WienGAGT/14
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/WienGAGT/14/
 ">Random character varieties</a>\nby Emmanuel Breuillard (Oxford) as part 
 of Vienna Geometry and Analysis on Groups Seminar\n\n\nAbstract\nConsider 
 a random group \\(\\Gamma\\) with \\(k\\) generators and \\(r\\) random re
 lators of large length \\(N\\). We ask about the geometry of the character
  variety of \\(\\Gamma\\) with values in \\(\\mathrm{SL}(2\,\\mathbb{C})\\
 ) or any semisimple Lie group \\(G\\). \nThis is the moduli space of group
  homomorphisms from \\(\\Gamma\\) to \\(G\\) up to conjugation. \nWe show 
 that with an exponentially small proportion of exceptions the character va
 riety is empty\, \\(k\\lt r+1\\)\, finite and large\, \\(k=r+1\\)\, or irr
 educible of dimension \\((k-r-1) \\mathrm{dim}\\thinspace G\\)\, \\(k\\gt 
 r+1\\). The proofs use new results on expander graphs for finite simple gr
 oups of Lie type and are conditional of the Riemann hypothesis.\n
LOCATION:https://researchseminars.org/talk/WienGAGT/14/
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