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UID:018b1a73fcf0010dbc3f3f5f6b68420a
CATEGORIES:Colloquia
CREATED:20210331T101537
SUMMARY:Unipotent flows on hyperbolic manifolds, à la Ratner
LOCATION:Zoom
DESCRIPTION:Abstract: The celebrated Ratner's orbit closure theorem proved around 1990 
 says that in a homogeneous space of finite volume, the closure of an orbit 
 of any subgroup generated by unipotent flows is homogeneous. A special case
  of Ratner’s theorem (also proved by Shah independently) implies that the c
 losure of a geodesic plane in a hyperbolic manifold of finite volume is alw
 ays a properly immersed submanifold. Searching for analogs of Ratner's theo
 rem in the infinite volume setting is a major challenge. We present a conti
 nuous family of hyperbolic 3-manifolds, and a countable family of higher di
 mensional hyperbolic manifolds of infinite volume, for which we have an ana
 logue of Ratner’s theorem.\n \n (Based on joint work with McMullen, Mohamma
 di, Benoist and Lee in different parts.)\n
X-ALT-DESC;FMTTYPE=text/html:<p style="background: white;">Abstract: The celebrated Ratner's orbit closu
 re theorem proved around 1990 says that in a homogeneous space of finite vo
 lume, the closure of an orbit of any subgroup generated by unipotent flows 
 is homogeneous. A special case of Ratner’s theorem (also proved by Shah ind
 ependently) implies that the closure of a geodesic plane in a hyperbolic ma
 nifold of finite volume is always a properly immersed submanifold. Searchin
 g for analogs of Ratner's theorem in the infinite volume setting is a major
  challenge. We present a continuous family of hyperbolic 3-manifolds, and a
  countable family of higher dimensional hyperbolic manifolds of infinite vo
 lume, for which we have an analogue of Ratner’s theorem.<br /> <br /> (Base
 d on joint work with McMullen, Mohammadi, Benoist and Lee in different part
 s.)</p>
CONTACT:Hee Oh (Yale)
DTSTAMP:20260829T020443
DTSTART;TZID=America/New_York:20210407T153000
DTEND;TZID=America/New_York:20210407T163000
SEQUENCE:0
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