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Colóquio de Alunos

Título |
Combinatorial applications of Borsuk-Ulam theorem |

Expositor |
Walner Mendonça
IMPA |

Data |
Sexta-feira, 11 de outubro de 2019, 15:30 |

Local |
Auditorio 1 |

Resumo |

The Borsuk–Ulam theorem states that for every continuous function $f:\mathbb{S}^d \rightarrow \mathbb{R}^d$, there exists $x \in \mathbb{S}^d$ such that $f(x) = f(-x)$. In 1978, the Hungarian mathematician László Lovász brilliantly used the Borsuk–Ulam theorem to give a solution to a 23 years old conjecture due to Kneser about the chromatic number of a specific family of graphs. That proof gave birth to what nowadays is known as the topological method in combinatorics. In this talk, we will see Lovász's proof of Kneser's conjecture and some other applications of the Borsuk–Ulam theorem in combinatorics.