## Contact Info

Pure MathematicsUniversity of Waterloo

200 University Avenue West

Waterloo, Ontario, Canada

N2L 3G1

Departmental office: MC 5304

Phone: 519 888 4567 x33484

Fax: 519 725 0160

Email: puremath@uwaterloo.ca

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Monday, July 29, 2013 — 11:30 AM EDT

For a set of numbers A, let the sum-set A + A denote {a1 + a2 : a1, a2 ∈ A}. Freiman’s theorem proves the remarkable notion that if a finite subset of integers A has a relatively small sum-set A + A, then A essentially resembles an arithmetic progression. More precisely, if |A + A| ≤ C|A| then there exists constants d, S depending only on C such that A is contained in a generalized arithmetic progression of dimension d and size ≤ S|A|. This is the first of two talks presenting the proof of Freiman’s theorem, which uses ideas ranging from graph theory, discrete Fourier analysis, and Minkowski’s geometry of numbers. For a set of numbers A, let the sum-set A + A denote {a1 + a2 : a1,a2 ∈ A}. Freiman’s theorem proves the remarkable notion that if a finite subset of integers A has a relatively small sum-set A + A, then A essentially resembles an arithmetic progression. More precisely, if |A+A| ≤ C|A| then there exists constants d,S depending only on C such that A is contained in a generalized arithmetic progression of dimension d and size ≤ S|A|. This is the first of two talks presenting the proof of Freiman’s theorem, which uses ideas ranging from graph theory, discrete Fourier analysis, and Minkowski’s geometry of numbers.

Location

MC - Mathematics & Computer Building

5046

200 University Avenue West

Waterloo, ON N2L 3G1

Canada

200 University Avenue West

Waterloo, ON N2L 3G1

Canada

University of Waterloo

200 University Avenue West

Waterloo, Ontario, Canada

N2L 3G1

Departmental office: MC 5304

Phone: 519 888 4567 x33484

Fax: 519 725 0160

Email: puremath@uwaterloo.ca

University of Waterloo

University of Waterloo

43.471468

-80.544205

200 University Avenue West

Waterloo,
ON,
Canada
N2L 3G1