<div dir="ltr"><div class="gmail_quote"><br><div dir="ltr"><p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:Calibri,"sans-serif""><span lang="EN-US" style="font-size:12pt;line-height:115%"> </span></p>
<p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:Calibri,"sans-serif""><span lang="EN-US" style="font-size:12pt;line-height:115%">Dear colleagues, </span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0.0001pt;text-align:justify;line-height:normal;font-size:11pt;font-family:Calibri,"sans-serif""><span lang="EN-US" style="font-size:12pt">Our next seminar will be
held on Monday, <b>June 19</b>,<b> </b>from <b>3:30
p.m. to 4:30 p.m</b>. (Rio de Janeiro local time). This meeting will take place at room </span><b><span lang="EN-US" style="font-size:12pt">C116
- Bloco C - CT</span></b><b><span lang="DE" style="font-size:12pt"> – Instituto de Matemática – UFRJ. </span></b><span lang="DE" style="font-size:12pt">There will be no transmission
online.</span><b><span lang="EN-US" style="font-size:12pt"></span></b></p>
<p class="MsoNormal" style="line-height:12.65pt;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial;margin:0cm 0cm 10pt;font-size:11pt;font-family:Calibri,"sans-serif""><span lang="EN-US" style="font-size:12pt"> </span></p>
<p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:Calibri,"sans-serif""><span lang="EN-US" style="font-size:12pt;line-height:115%">Speaker: </span><b><span lang="EN-US" style="font-size:12pt;line-height:115%;color:black">Taísa Lopes
Martins (IME-UFF)</span></b><b><span lang="EN-US" style="font-size:12pt;line-height:115%"></span></b></p>
<p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:Calibri,"sans-serif""><span lang="EN-US" style="font-size:12pt;line-height:115%">Title: </span><b><span lang="EN-US" style="font-size:12pt;line-height:115%">A Lower
bound for set-colouring Ramsey numbers</span></b><span lang="EN-US" style="font-size:12pt;line-height:115%"></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0.0001pt;line-height:normal;font-size:11pt;font-family:Calibri,"sans-serif""><span lang="EN-US" style="font-size:12pt"> </span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0.0001pt;line-height:normal;font-size:11pt;font-family:Calibri,"sans-serif""><span lang="EN-US" style="font-size:12pt">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. </span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0.0001pt;line-height:normal;font-size:11pt;font-family:Calibri,"sans-serif""><span lang="EN-US" style="font-size:12pt"> </span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0.0001pt;line-height:normal;font-size:11pt;font-family:Calibri,"sans-serif""><span lang="EN-US" style="font-size:12pt">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^{</span><span style="font-size:12pt">Θ</span><span lang="EN-US" style="font-size:12pt">(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.</span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0.0001pt;line-height:normal;font-size:11pt;font-family:Calibri,"sans-serif""><span lang="EN-US" style="font-size:12pt"> </span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0.0001pt;line-height:normal;font-size:11pt;font-family:Calibri,"sans-serif""><span lang="EN-US" style="font-size:12pt">This is a joint work with Lucas Aragão, Maurício Collares, João Pedro
Marciano and Rob Morris.</span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0.0001pt;line-height:normal;font-size:11pt;font-family:Calibri,"sans-serif""><span lang="EN-US" style="font-size:12pt"> </span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0.0001pt;line-height:normal;font-size:11pt;font-family:Calibri,"sans-serif""><b><span lang="EN-US" style="font-size:12pt;color:black"> </span></b></p>
<p class="MsoNormal" style="margin:0cm 0cm 0.0001pt;line-height:normal;font-size:11pt;font-family:Calibri,"sans-serif""><b><span lang="EN-US" style="font-size:12pt;color:black"> </span></b></p>
<p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:Calibri,"sans-serif""><span lang="EN-US" style="font-size:12pt;line-height:115%">More complete information
about the seminars can be found at</span></p>
<p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:Calibri,"sans-serif""><span style="font-size:12pt;line-height:115%"><a href="http://www.dme.ufrj.br/?page_id=3355" style="color:blue" target="_blank"><span lang="EN-US" style="color:windowtext;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">http://www.dme.ufrj.br/?page_id=3355</span></a></span><span lang="EN-US" style="font-size:12pt;line-height:115%"></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:Calibri,"sans-serif""><span style="font-size:12pt;line-height:115%">Sincerely, </span></p>
<p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:Calibri,"sans-serif""><span style="font-size:12pt;line-height:115%">Giulio Iacobelli e Maria Eulalia Vares</span></p>
<p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:Calibri,"sans-serif""><span style="font-size:12pt;line-height:115%"> </span></p>
<p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:Calibri,"sans-serif""><span style="font-size:12pt;line-height:115%"> </span></p></div>
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