[ABE-L] Seminário de Probabilidade - IM-UFRJ - 19 de junho - 15:30

[Maria Eulalia Vares]

Dear colleagues,

Our next seminar will be held on Monday, *June 19*, from *3:30 p.m. to 4:30
p.m*. (Rio de Janeiro local time).  This meeting will take place at room *C116
- Bloco C - CT** – Instituto de Matemática – UFRJ. *There will be no
transmission online.



Speaker:   *Taísa Lopes Martins (IME-UFF)*

Title:   *A Lower bound for set-colouring Ramsey numbers*



Abstract: The set-colouring Ramsey number Rr,s(k) is defined to be the
minimum n such that if each edge of the complete graph Kn is assigned a set
of s colours from {1, . . . , r}, then one of the colours contains a
monochromatic clique of size k. The case s = 1 is the usual r-colour Ramsey
number, and the case s = r − 1 was studied by Erdős, Hajnal and Rado in
1965, and by Erdős and Szemerédi in 1972.



The first significant results for general s were obtained only recently, by
Conlon, Fox, He, Mubayi, Suk and Verstraëte, who showed that Rr,s(k) =
2^{Θ(kr)}
if s/r is bounded away from 0 and 1. In the range s = r − o(r), however,
their upper and lower bounds diverge significantly. In this talk we
introduce a new (random) colouring, and use it to determine Rr,s(k) up to
polylogarithmic factors in the exponent for essentially all r, s and k.



This is a joint work with Lucas Aragão, Maurício Collares, João Pedro
Marciano and Rob Morris.







More complete information about the seminars can be found at

http://www.dme.ufrj.br/?page_id=3355

Sincerely,

Giulio Iacobelli e Maria Eulalia Vares
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