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SUMMARY:Dimension of Self-similar Measures and Additive Combinatorics - Ho
 chman\, M (Hebrew University of Jerusalem)
DTSTART:20140702T090000Z
DTEND:20140702T095000Z
UID:TALK53283@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:I will discuss recent progress on the problem of computing the
  dimension of a self-similar set or measure in $mathbb{R}$ in the presence
  of non-trivial overlaps. It is thought that unless the overlaps are "exac
 t" (an essentially algebraic condition)\, the dimension achieves the trivi
 al upper bound. I will present a weakened version of this that confirms th
 e conjecture in some special cases. A key ingredient is a theorem in addit
 ive combinatorics that describes in a statistical sense the structure of m
 easures whose convolution has roughly the same entropy at small scales as 
 the original measure. As time permits\, I will also discuss the situation 
 in $mathbb{R}^d$.\n
LOCATION:Seminar Room 1\, Newton Institute
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