Limits of discrete structures

Course guarantor:

Jan Volec

Lecturer:

Jan Volec

Tutor:

Supervisor:

Department of Mathematics

Synopsis:

Requirements:

Syllabus of lectures:

1. Graph homomorphism, Graph algebras

2. Szemerédi regularity lemma and its applications in discrete mathematics

3. Property testing

4. Cut metric, analytical representation of graph limits (graphons)

5. Subgraph counting and the left convergence

6. Generalized colorings and the right convergence

7. Graphon entropy and the large deviation principle

8. Semidefinite programming, flag algeras

9. Limits of hypergraphs, limits of tournaments, limits of permutations

Syllabus of tutorials:

Study Objective:

Study materials:

Course textbook:

[1] L. Lovász: Large Networks and Graph Limits, American Mathematical Society, 2012.

Additional material:

[2] N. Alon, J. Spencer: The Probabilistic Method, Wiley, 2016.

[3] Y. Zhao: Graph Theory and Additive Combinatorics, Cambridge University Press, 2023.

Note:

Time-table for winter semester 2024/2025:

Time-table is not available yet

Time-table for summer semester 2024/2025:

Time-table is not available yet

The course is a part of the following study plans: