Additive Number Theory

General characterization

Prerequisites

Available soon

Bibliography

A.Geroldinger and I.Z. Ruzsa, Combinatorial Number Theory and Additive Group Theory, Birkhäuser, 2009.

B.M. Landman and A. Robertson, A. Ramsey Theory on the Integers, American Mathematical Society, 2004.

M.B. Nathanson, Additive Number Theory: Inverse problems and the geometry of sumsets, Springer, 1996.

T. Tao and V. Vu, Additive Combinatorics, Cambridge Univ. Press, 2006.

Teaching method

Tutorial: one hour discussion of the student readings.

Evaluation method

Weekly presentations. List of Problems. Final project.

Subject matter

Part 1.
Sum set estimates.
Structure of sets with few sums.
Density and structure.
Inverse sumset theorems.
Ramsey theory on the integers.

Part 2.
The probabilistic method.
Additive geometry.
Graph theoretic methods.
Incidence geometry.
Algebraic methods.

Programs

Programs where the course is taught: