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SUMMARY:Ilya Kapovich (CUNY)
DTSTART:20200428T143000Z
DTEND:20200428T153000Z
DTSTAMP:20260423T022731Z
UID:SGG/1
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/SGG/1/">Sing
 ularity properties of random free group automorphisms and of random trees 
 in the boundary of Outer space</a>\nby Ilya Kapovich (CUNY) as part of Sé
 minaire de groupes et géométrie\n\n\nAbstract\nIt is known that\, under 
 mild assumptions\, for a free group $F_r$ of finite rank $r>2$\, a "random
 " element $\\phi_n\\in Out(F_r)$\, obtained after $n$ steps of a random wa
 lk on $Out(F_r)$\, is fully irreducible (a free group analog of being pseu
 doAnosov)\,\nand that an a.e. trajectory of the way converges to a point i
 n the boundary of the CullerVogtmann Outer space $CV_r$. We prove that gen
 erically the attracting $\\mathbb R$-tree $T_+(\\phi_n)\\in \\partial CV_r
 $ for such a random fully irreducible $\\phi_n$ is trivalent (that is\, al
 l branch points of $T_+$ have degree 3) and nongeometric\, (that is $T_+$ 
 is not the dual tree of any measured foliation of a finite 2-complex).\n\n
 Similarly\, for the exit/harmonic\nmeasure $\\nu$ of the random walk on th
 e boundary $\\partial CV_r$ of the Outer space\, we prove that a $\\nu$-a.
 e. $\\mathbb R$-tree $T\\in \\partial CV_r$ is trivalent and nongeometric.
 \nThe talk is based on joint work with Joseph Maher\, Catherine Pfaff and 
 Samuel Taylor.\n
LOCATION:https://researchseminars.org/talk/SGG/1/
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