Additive Number Theory
Manuel Almeida Silva
Weekly - Available soon
Total - 20
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.
Tutorial: one hour discussion of the student readings.
Weekly presentations. List of Problems. Final project.
Sum set estimates.
Structure of sets with few sums.
Density and structure.
Inverse sumset theorems.
Ramsey theory on the integers.
The probabilistic method.
Graph theoretic methods.