BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Talks.cam//talks.cam.ac.uk//
X-WR-CALNAME:Talks.cam
BEGIN:VEVENT
SUMMARY:Equidistribution of divergent orbits in the space of lattices -  O
 fir David (Hebrew university\, Jerusalem)
DTSTART:20180220T130000Z
DTEND:20180220T140000Z
UID:TALK101575@talks.cam.ac.uk
CONTACT:HoD Secretary\, DPMMS
DESCRIPTION: A well known application of the pointwise ergodic theorem (PE
 T) states that almost every x in [0\,1] has a normal continued fraction ex
 pansion\, or equivalently its orbit under the Gauss map T(x):={1/x} (where
  {y} is the fractional part of y) equidistributes with respect to the Gaus
 s Kuzmin measure dt/( ln(2)(1+t) ). This is not true for all x\, and in pa
 rticular it fails for rational numbers which have finite continued fractio
 n expansions.\n\nIn this talk we shall see how to "extend" the PET to rati
 onal numbers and its connection to divergent orbits of the diagonal group 
 in the space of 2-dimensional lattices. Furthermore\, we shall show how th
 e natural setting of this problem is actually over the adeles\, and in par
 ticular it can be formulated in any dimension (for which we give some part
 ial results).\n\nThis is a joint work with Uri Shapira from the Technion.\
 n
LOCATION:MR13 (EL.05)
END:VEVENT
END:VCALENDAR