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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Dimension of Self-similar Measures and Additive Co
mbinatorics - Hochman\, M (Hebrew University of Je
rusalem)
DTSTART;TZID=Europe/London:20140702T100000
DTEND;TZID=Europe/London:20140702T105000
UID:TALK53283AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/53283
DESCRIPTION:I will discuss recent progress on the problem of c
omputing the dimension of a self-similar set or me
asure in $mathbb{R}$ in the presence of non-trivia
l overlaps. It is thought that unless the overlaps
are "exact" (an essentially algebraic condition)\
, the dimension achieves the trivial upper bound.
I will present a weakened version of this that con
firms the conjecture in some special cases. A key
ingredient is a theorem in additive combinatorics
that describes in a statistical sense the structur
e of measures whose convolution has roughly the sa
me entropy at small scales as the original measure
. As time permits\, I will also discuss the situat
ion in $mathbb{R}^d$.\n
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:Mustapha Amrani
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