Sum-set problems and results -- Old and new
Béla Bollobás (University of Cambridge and University of Memphis)

Sums of subsets of R^n, Z^n and Z_p^n have been studied for well over a century, although at the beginning progress was very slow. The subject took off in the 1960s, when Erdos and Heilbronn, and Freimann published their celebrated papers, and has been going from strength to strength with the results of Gowers, Green, Károlyi, Ruzsa, Tao, Vu and others. The talk, which should be understandable to a wide audience, not only to pure mathematicians, will contain some of the results I have obtained with Imre Leader and Marius Tiba, together with a recent breakthrough achieved by Gowers, Green, Manners and Tao.