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PRODID:-//Columba Systems Ltd//NONSGML CPNG/SpringViewer/ICal Output/3.3-
M3//EN
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METHOD:PUBLISH
BEGIN:VEVENT
DTSTAMP:20200217T103637Z
DTSTART:20200217T150000Z
DTEND:20200217T160000Z
SUMMARY:Projections of random measures on products of $\\times m\,\\times
n$-invariant sets and a random Furstenberg sumset conjecture - Dynamica
l Systems and Analysis Seminar Series
UID:{http://www.columbasystems.com/customers/uom/gpp/eventid/}if3-k62eq9k
3-y7vfe1
DESCRIPTION:Catherine Bruce will be speaking at this research seminar\, p
art of the Dynamical Systems and Analysis seminar series. Abstract: In
2012 Hochman and Shmerkin proved that\, given Borel probability measures
on [0\,1] invariant under multiplication by 2 and 3 respectively\, the
Hausdorff dimension of the orthogonal projection of the product of these
measures is equal to the maximum possible value in every direction exce
pt the horizontal and vertical directions. Their result holds beyond mul
tiplication by 2\,3 to natural numbers m\,n which are multiplicatively i
ndependent. We discuss a generalisation of this theorem to include rando
m cascade measures on subsets of [0\,1] invariant under multiplication b
y multiplicatively independent m\,n. We will define random cascade measu
res in a heuristic way\, as a natural randomisation of invariant measure
s on symbolic space. The theorem of Hochman and Shmerkin fully resolved
a conjecture of Furstenberg originating in the late 1960s concerning sum
sets of these invariant sets. We apply our main result to present a rand
om version of this conjecture which holds for products of percolations o
n $\\times m\, \\times n$-invariant sets.\n
STATUS:TENTATIVE
TRANSP:TRANSPARENT
CLASS:PUBLIC
LOCATION:G.113\, Alan Turing Building\, Manchester
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