What is… Ramsey theory?

Manuel Silva, Universidade Nova de Lisboa, Portugal

23 de Junho de 2021, 16 horas no endereço Zoom:

https://videoconf-colibri.zoom.us/j/83030580321?pwd=Z3VLNjc0c3VXUHNqQWtLN1ZPaHY1QT09

ID: 830 3058 0321 | Palavra chave: xyz

Resumo/Abstract: In 1928 Frank P. Ramsey, motivated by philosophical considerations, proved a theorem in his paper “On a problem of formal logic”. This result can be viewed as a powerful generalization of the pigeonhole principle and implies that every large combinatorial structure contains some regular substructure. Since then, Ramsey Theory has become an important area of combinatorics with connections to other fields of mathematics such as number theory, ergodic theory, mathematical logic, and graph theory. In the same spirit, Van der Waerden proved in 1927 a regularity result about partitions of the natural numbers. We will see several examples of Ramsey-type results, trying in each case to find some order in a large combinatorial system.

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