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Additive Combinatorics and Applications
Last Updated: 2026-02-05 16:14:51
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
- DR
Examination
- Type
- ungraded semester performance
Registration & Places
Course Components
| Type | Title | Time & Place | Hours |
|---|---|---|---|
| lecture with exercise | Additive Combinatorics and Applications |
|
4 h weekly |
Offered In
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Doctorate Mathematics (More Information at: )
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Subject Specialisation (The list of courses (together with the allocated credit points) eligible for doctoral students is published each semester in the newsletter of the ZGSM.)
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Graduate School (Official website of the Zurich Graduate School in Mathematics: )
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