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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Towards an entropy-based sumset calculus for addit
ive combinatorics and convex geometry - Madiman\,
M (Yale)
DTSTART;TZID=Europe/London:20110615T153000
DTEND;TZID=Europe/London:20110615T163000
UID:TALK31742AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/31742
DESCRIPTION:We use common entropy-based tools to study two kin
ds of problems: the first of proving general cardi
nality inequalities for sumsets in possibly nonabe
lian groups\, and the second of proving volume ine
qualities of interest in convex geometry and geome
tric functional analysis. We will spend most of ou
r time on the discrete setting (joint work with A.
Marcus and P. Tetali)\, introducing the notion of
partition-determined functions\, and presenting s
ome basic new inequalities for the entropy of such
functions of independent random variables\, as we
ll as for cardinalities of compound sets obtained
using these functions. Corollaries of the results
for partition-determined functions include entropi
c analogues of general Pl"unnecke-Ruzsa type inequ
alities\, sumset cardinality inequalities in abeli
an groups generalizing inequalities of Gyarmati-Ma
tolcsi-Ruzsa and Balister-Bollob'as\, and partial
progress towards a conjecture of Ruzsa for sumsets
in nonabelian groups. Time permitting\, we will a
lso mention some results in the continuous setting
(joint work with S. Bobkov) including some Pl"unn
ecke-type inequalities for Minkowski sums of conve
x sets\, and an entropic generalization of V. Milm
an's reverse Brunn-Minkowski inequality. \n
LOCATION:Seminar Room 2\, Newton Institute Gatehouse
CONTACT:Mustapha Amrani
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