BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Talks.cam//talks.cam.ac.uk//
X-WR-CALNAME:Talks.cam
BEGIN:VEVENT
SUMMARY:Towards an entropy-based sumset calculus for additive combinatoric
 s and convex geometry - Madiman\, M (Yale)
DTSTART:20110615T143000Z
DTEND:20110615T153000Z
UID:TALK31742@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:We use common entropy-based tools to study two kinds of proble
 ms: the first of proving general cardinality inequalities for sumsets in p
 ossibly nonabelian groups\, and the second of proving volume inequalities 
 of interest in convex geometry and geometric functional analysis. We will 
 spend most of our time on the discrete setting (joint work with A. Marcus 
 and P. Tetali)\, introducing the notion of partition-determined functions\
 , and presenting some basic new inequalities for the entropy of such funct
 ions of independent random variables\, as well as for cardinalities of com
 pound sets obtained using these functions. Corollaries of the results for 
 partition-determined functions include entropic analogues of general Pl"un
 necke-Ruzsa type inequalities\, sumset cardinality inequalities in abelian
  groups generalizing inequalities of Gyarmati-Matolcsi-Ruzsa and Balister-
 Bollob'as\, and partial progress towards a conjecture of Ruzsa for sumsets
  in nonabelian groups. Time permitting\, we will also mention some results
  in the continuous setting (joint work with S. Bobkov) including some Pl"u
 nnecke-type inequalities for Minkowski sums of convex sets\, and an entrop
 ic generalization of V. Milman's reverse Brunn-Minkowski inequality. \n
LOCATION:Seminar Room 2\, Newton Institute Gatehouse
END:VEVENT
END:VCALENDAR