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SUMMARY:Divisibility properties in higher rank lattices - Mozes\, S (Hebre
 w University of Jerusalem)
DTSTART:20140630T090000Z
DTEND:20140630T095000Z
UID:TALK53242@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:In a joint work with Manfred Einsiedler we discuss a relations
 hip between the dynamical properties of a maximal diagonalizable group $A$
  on certain arithmetic quotients and arithmetic properties of the lattice.
  In particular\, we consider the semigroup of all integer quaternions unde
 r multiplication. For this semigroup we use measure rigidity theorems to p
 rove that the set of elements that are not divisible by a given reduced qu
 aternion is very small:\nWe show that any quaternion that has a sufficient
 ly divisible norm is also divisible by the given quaternion. Restricting t
 o the quaternions that have norm equal to products of powers of primes fro
 m a given list (containing at least two) we show that the set of exception
 s has subexponential growth.\n\n
LOCATION:Seminar Room 1\, Newton Institute
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