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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Divisibility properties in higher rank lattices -
Mozes\, S (Hebrew University of Jerusalem)
DTSTART;TZID=Europe/London:20140630T100000
DTEND;TZID=Europe/London:20140630T105000
UID:TALK53242AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/53242
DESCRIPTION:In a joint work with Manfred Einsiedler we discuss
a relationship between the dynamical properties o
f a maximal diagonalizable group $A$ on certain ar
ithmetic quotients and arithmetic properties of th
e lattice. In particular\, we consider the semigro
up of all integer quaternions under multiplication
. For this semigroup we use measure rigidity theor
ems to prove that the set of elements that are not
divisible by a given reduced quaternion is very s
mall:\nWe show that any quaternion that has a suff
iciently divisible norm is also divisible by the g
iven quaternion. Restricting to the quaternions th
at have norm equal to products of powers of primes
from a given list (containing at least two) we sh
ow that the set of exceptions has subexponential g
rowth.\n\n
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:Mustapha Amrani
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