Georgia Institute of Technology College of Sciences

The entropy function has a number of nice properties that make it a useful counting tool, especially when one wants to bound a set with respect to the set's projections. In this talk, I will show a method developed by Mokshay Madiman, Prasad Tetali, and myself that builds on the work of Gyarmati, Matolcsi and Ruzsa as well as the work of Ballister and Bollobas. The goal will be to give a black-box method for generating projection bounds and to show some applications by giving new bounds on the sizes of Abelian and non-Abelian sumsets.