Additive Number Theory
Code
11637
Academic unit
Faculdade de Ciências e Tecnologia
Department
Departamento de Matemática
Credits
6.0
Teacher in charge
Oleksiy Karlovych
Teaching language
Português
Objectives
At the end of this course students will have acquired basic knowledge and skills in the area of Additive Number Theory in order to:
- Understand advanced contents in the area;
- Being able to start research on a topic in the area.
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.
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.