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SUMMARY:Ilya Kapovich (CUNY)
DTSTART:20200428T143000Z
DTEND:20200428T153000Z
DTSTAMP:20260404T132230Z
UID:SGG/1
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/SGG/1
 /">Singularity properties of random free group automorphisms and of random
  trees in the boundary of Outer space</a>\nby Ilya Kapovich (CUNY) as part
  of Séminaire 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 ra
 ndom walk on $Out(F_r)$\, is fully irreducible (a free group analog of bei
 ng pseudoAnosov)\,\nand that an a.e. trajectory of the way converges to a 
 point in the boundary of the CullerVogtmann Outer space $CV_r$. We prove t
 hat generically the attracting $\\mathbb R$-tree $T_+(\\phi_n)\\in \\parti
 al CV_r$ for such a random fully irreducible $\\phi_n$ is trivalent (that 
 is\, all 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-comple
 x).\n\nSimilarly\, for the exit/harmonic\nmeasure $\\nu$ of the random wal
 k on the 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 nongeo
 metric.\nThe talk is based on joint work with Joseph Maher\, Catherine Pfa
 ff and Samuel Taylor.\n
LOCATION:https://stable.researchseminars.org/talk/SGG/1/
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