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CATEGORIES:dg443's list
SUMMARY:Stability results for the semisum of sets in R^n -
Alessio Figalli - UT Austin
DTSTART;TZID=Europe/London:20140519T150000
DTEND;TZID=Europe/London:20140519T160000
UID:TALK52736AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/52736
DESCRIPTION:Given a Borel A in R^n of positive measure\, one c
an consider its semisum S=(A+A)/2. It is clear tha
t S contains A\, and it is not difficult to prove\
nthat they have the same measure if and only if A
is equal to his convex\nhull minus a set of measur
e zero. We now wonder whether this statement is st
able: \nif the measure of S is close to the one of
A\, is A close to his convex hull? More generally
\, one\nmay consider the semisum of two different
sets A and B\, in which case our question correspo
nds to proving a stability result for the Brunn-Mi
nkowski inequality. When n=1\, one can approximate
a set with finite unions of intervals to translat
e the problem to the integers Z. In this discrete
setting the question becomes a well-studied probl
em in additive combinatorics\, usually known as Fr
eiman's Theorem.\nIn this talk I will review some
results in the one-dimensional discrete\nsetting a
nd describe how to answer to the problem in arbitr
ary dimension.
LOCATION:MR14
CONTACT:
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