Séminaire CAESAR
de combinatoire additive
Séance du 10 février 2011
(11 heures, École polytechnique, CMLS, salle
de conférence):
Tom SANDERS
(Cambridge, G.B.)
Between Freiman's theorem and the Polynomial Freiman-Ruzsa conjecture
Freiman's theorem describes the structure of sets of integers having small doubling which enjoys
numerous applications in additive combinatorics. While the result is qualitatively comprehensive, a truer
picture is suggested by the Polynomial Freiman-Ruzsa conjecture, and in this talk we shall discuss how a
remarkable new technique of Croot and Sisask can be used in conjunction with a trick of Lopez and Ross to
provide much clearer quantitative information. We shall focus on the model finite field setting where there
are few prerequisites and the details are the cleanest.
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