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SUMMARY:Minju Lee (Yale University)
DTSTART:20210308T171500Z
DTEND:20210308T183000Z
DTSTAMP:20260423T021931Z
UID:NEDNT/20
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/20/">O
 rbit closures of unipotent flows for hyperbolic manifolds with Fuchsian en
 ds</a>\nby Minju Lee (Yale University) as part of New England Dynamics and
  Number Theory Seminar\n\nLecture held in Online.\n\nAbstract\nThis is joi
 nt work with Hee Oh. We establish an analogue of Ratner’s orbit closure 
 theorem for any connected closed subgroup generated by unipotent elements 
 in $\\mathrm{SO}(d\,1)$ acting on the space $\\Gamma\\backslash\\mathrm{SO
 }(d\,1)$\, assuming that the associated hyperbolic manifold $M=\\Gamma\\ba
 ckslash\\mathbb{H}^d$ is a convex cocompact manifold with Fuchsian ends. F
 or $d = 3$\, this was proved earlier by McMullen\, Mohammadi and Oh. In a 
 higher dimensional case\, the possibility of accumulation on closed orbits
  of intermediate subgroups causes serious issues\, but in the end\, all or
 bit closures of unipotent flows are relatively homogeneous. Our results im
 ply the following: for any $k\\geq 1$\,\n(1) the closure of any $k$-horosp
 here in $M$ is a properly immersed submanifold\;\n(2) the closure of any g
 eodesic $(k+1)$-plane in $M$ is a properly immersed submanifold\;\n(3) an 
 infinite sequence of maximal properly immersed geodesic $(k+1)$-planes int
 ersecting $\\mathrm{core} M$ becomes dense in $M$.\n
LOCATION:https://researchseminars.org/talk/NEDNT/20/
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