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Additive Combinatorics and Applications
Last Updated: 2026-02-05 16:14:49
Abstract
This course will be an introduction to the field of "additive combinatorics" and to its applications, especially to number theory and analysis.
Content
The topics which will be presented include: (1) Approximate subgroups, Sidon sets, and other types of structured sets (2) Existence and density of 3-term arithmetic progressions in abelian groups (3) The "structure vs randomness" dichotomy (4) The sum-product phenomenon and its generalizations (5) Gowers norms and arithmetic progressions of length 4 and more (6) Transfer principles and 3-term progressions in the primes (7) A survey of interactions of additive combinatorics with other fields, especially ergodic theory, and of some applications.
Resources
Lecture Notes
Lectures notes will be prepared and made available during the class.
Literature
T. Tao and V. Vu: "Additive combinatorics", Cambridge University Press K. Soundararajan: "Additive combinatorics", lectures notes, Stanford University, 2007; https://math.stanford.edu/~ksound/Notes.pdf Moreover, lectures notes will be prepared and made available during the class.
Learning Materials (Links)
- Main link
- Information
General Information
- Language
- English
- Levels
- BSC , MSC
Examination
- Type
- session examination
- Mode
- written 120 minutes
- Aids
- None
Course Components
| Type | Title | Time & Place | Hours |
|---|---|---|---|
| lecture with exercise | Additive Combinatorics and Applications |
|
4 h weekly |
Offered In
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Electives (For the Master's degree in Applied Mathematics the following additional condition (not manifest in myStudies) must be obeyed: At least 14 of the required 26 credits from core courses and electives must be acquired in areas of applied mathematics and further application-oriented fields.)
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