Additive combinatorics is the study of additive questions about finite sets of integers. Possible topics include the theorems of Roth and Szemerédi (on additive progressions in dense sets of integers), Freiman's theorem and its relatives (on the structure of sumsets that are almost closed under addition), sum-product phenomena, and the Littlewood-Offord problem. A particular aim of the course will be to give a taster of the varied methods which have been brought to bear on the subject: Fourier analysis, polynomial methods, probabilistic methods, methods from information theory, graph theory and incidence geometry.
Target group: PhD students and postdocs.
Prerequisites: None
Evaluation: Problem sheets
Teaching format: None
ECTS: 3 Year: 2025
Track segment(s):
Elective
Teacher(s):
Matthew Kwan
Tim Browning
Teaching assistant(s):
- Teacher: Tim Browning
- Teacher: Matthew Alan KWAN