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Quasirandomness and Regularity
Last Updated: 2026-02-05 14:59:53
Abstract
This course focuses on developing "working knowledge" of quasirandomness and regularity for several classes of combinatorial objects: graphs, permutations, Abelian groups, hypergraphics, and others as time permits.
Content
We will introduce and discuss the areas of quasirandomness and regularity, the intimate connections between them, and applications. Both subjects have been very active areas in the past ten years, and there are many open problems and topics of study still to be addressed. This course will focus on developing "working knowledge" of quasirandomness and regularity for several classes of combinatorial objects: graphs, permutations, Abelian groups, hypergraphs, and others as time permits. We will spend the first half of the course studying the definitions and basic theorems in these contexts, beginning with the series of discoveries by Chung and Graham in the early 1990's. The second half will consist of more in-depth topics, including applications to number theory, the seminal work of Simonovits-Sos, and recent developments in hypergraph regularity.
General Information
- Language
- English
- Frequency
- Yearly recurring
Examination
- Type
- end-of-semester examination
Course Components
| Type | Title | Time & Place | Hours |
|---|---|---|---|
| lecture | Quasirandomness and Regularity |
|
2 h weekly |
| lecture with exercise | Quasirandomness and Regularity |
|
1 h weekly |
| exercise | Quasirandomness and Regularity |
|
1 h weekly |