NSFCBMS Conference on Additive Combinatorics from a Geometric Viewpoint
Jozsef Solymosi
University of British Columbia http://www.math.ubc.ca/~solymosi/ 

Abstract 
Additive structures in subsets of integers
Hilbert cubes, Schur's theorem and other coloring questions. When can we expect density version of a coloring problem? Density of integer sequences. In additive combinatorics one of the basic questions what can we say about the structure of sets with small sumsets. A special case is when we are considering a partitioning of the first n integers into a few partition classes. (Or, colouring the integers, which is an equivalent formulation of the problem.) The oldest result is due to Hilbert, who proved that any coloring of the integers contains a "Hilbertcube". Schur's theorem points to stronger statements, however there the statements only hold for the coloring (partitioning) problems, no density variants hold. 