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SUMMARY:Sumset bounds for the entropy on abelian groups - Ioannis Kontoyia
 nnis (Engineering\, Cambridge)
DTSTART:20190129T140000Z
DTEND:20190129T150000Z
UID:TALK114322@talks.cam.ac.uk
CONTACT:Perla Sousi
DESCRIPTION:The development of the field of additive combinatorics in rece
 nt years has provided\, among other things\, a collection of fascinating a
 nd deep\, elementary tools for estimating the sizes of discrete subsets of
  abelian groups. Tao in 2010 connected these results with the entropy of d
 iscrete probability measures: Interpreting the entropy of a discrete rando
 m variable as the logarithm of its "effective support size\," he provided 
 a series of new inequalities for the discrete entropy. We will review this
  background and describe how Tao's results extend in a nontrivial way to t
 he entropy of random elements in general abelian groups. The somewhat surp
 rising key difference between the discrete and the general case is that th
 e "functional submodularity" property of the discrete entropy needs to be 
 replaced by the general "data processing property" of the entropy.\n\nNo b
 ackground in information theory\, entropy or additive combinatorics will b
 e assumed.
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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