**Date & Time:** Monday, August 13, 2012, 17:00-18:00

**Venue:** Ramanujan Hall

**Title:** An entropy-based sumset calculus for discrete and continuous settings

**Speaker:** Prof. Mokshay Madiman, Yale University, USA

**Abstract:** Additive combinatorics has been an area of rapid
mathematical development in the last decade, featuring major advances
such as the Green-Tao theorem on arbitrarily long arithmetic
progressions in the prime numbers. A key arsenal of tools in additive
combinatorics is the sumset calculus developed by Pl\"unnecke, Ruzsa
and Freiman, which investigates the cardinality behavior of the sumset
(Minkowski sum) of discrete subsets of an abelian group. Motivated
both by a desire to develop a more general probabilistic framework for
this calculus and by applications in information theory and
engineering, we present a sumset calculus based on entropy for sums of
independent random variables (either discrete taking values in an
arbitrary abelian group, or drawn from continuous distributions on a
Euclidean space). The talk relies on several collaborative efforts,
including with Ioannis Kontoyiannis (Athens University of Economics
and Business), Adam Marcus (Yale University), and Prasad Tetali
(Georgia Tech).

About the Speaker: Mokshay Madiman did B.Tech. in Electrical Engineering from IIT Bombay in 1999 and later obtained M.S. and Ph.D. in Applied Mathematics from Brown University, USA in the years 2001 and 2005 respectively. He is currently an Associate Professor in the Department of Statistics at Yale University. His research interest are primarily in the interplay of information theory with mathematics and statistics, particularly in the context of extremal problems. More information is available from his home page: http://www.stat.yale.edu/~mm888/