<div dir="ltr"><div class="gmail_quote"><div dir="ltr"><div><br></div><div>

<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>October 16</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="DE" style="font-size:12pt"> </span></p>

<p class="MsoNormal" style="line-height:normal;margin:0cm 0cm 10pt;font-size:11pt;font-family:Calibri,"sans-serif""><span style="font-size:12pt;color:black">Speaker: <b> Sergio
I. López  (</b></span><b>Universidad Nacional Autónoma de México</b>)</p>

<p class="MsoNormal" style="line-height:normal;margin:0cm 0cm 10pt;font-size:11pt;font-family:Calibri,"sans-serif""><span lang="EN-US" style="font-size:12pt;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">Title: </span><span lang="EN-US">Targeted cutting of random recursive
trees</span></p>

<p class="MsoNormal" style="line-height:normal;font-size:11pt;font-family:Calibri,"sans-serif""><span lang="EN-US" style="font-size:12pt;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">Abstract: </span><span lang="EN-US" style="font-size:12pt;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"> </span><span lang="EN-US" style="font-size:12pt">Increasing
trees are rooted trees, where each vertex has a unique label and the labels
along paths away from the root are in increasing order. A Random recursive tree
on </span><span style="font-size:12pt;font-family:"Cambria Math","serif"">𝑛</span><span lang="EN-US" style="font-size:12pt"> vertices (abbreviated as
RRTs) is a tree chosen uniformly at random from the set of increasing trees
with vertex labels {1,…,</span><span style="font-size:12pt;font-family:"Cambria Math","serif"">𝑛</span><span lang="EN-US" style="font-size:12pt">}. The idea of cutting
random recursive trees was introduced by Meir and Moon in 1974. They studied
the following procedure: Start with a random recursive tree on </span><span style="font-size:12pt;font-family:"Cambria Math","serif"">𝑛</span><span lang="EN-US" style="font-size:12pt"> vertices. Choose an edge at random and
remove it, along with the cut subtree that does not contain the root. Repeat
until the remaining tree consists only of the root; at which point, we say that
the tree has been deleted. </span></p>

<p class="MsoNormal" style="line-height:normal;margin:0cm 0cm 10pt;font-size:11pt;font-family:Calibri,"sans-serif""><span lang="EN-US" style="font-size:12pt">Let X be
the number of edge removals needed to delete a RRT with </span><span style="font-size:12pt;font-family:"Cambria Math","serif"">𝑛</span><span lang="EN-US" style="font-size:12pt"> vertices. The random variable X has been
thoroughly studied and analogous variables under distinct models of random
trees have been analyzed; in particular, X grows asymptotically as </span><span style="font-size:12pt;font-family:"Cambria Math","serif"">𝑛</span><span lang="EN-US" style="font-size:12pt"> ln(</span><span style="font-size:12pt;font-family:"Cambria Math","serif"">𝑛</span><span lang="EN-US" style="font-size:12pt">). In this talk we propose and study a method for cutting down a random
recursive tree that focuses on its largest degree vertices. Enumerate the
vertices of a random recursive tree of size </span><span style="font-size:12pt;font-family:"Cambria Math","serif"">𝑛</span><span lang="EN-US" style="font-size:12pt"> according to a decreasing order of their degrees. The targeted,
vertex-cutting process is performed by sequentially removing vertices according
to that order and keeping only the subtree containing the root after each
removal. The algorithm ends when the root is picked to be removed.</span></p>

<p class="MsoNormal" style="line-height:normal;margin:0cm 0cm 10pt;font-size:11pt;font-family:Calibri,"sans-serif""><span lang="EN-US">Joint work with Laura Eslava and Marco L.
Ortiz. </span><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"> </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;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"> </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%">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""><a href="http://www.dme.ufrj.br/?page_id=3398" style="color:rgb(5,99,193)" target="_blank"><span lang="EN-US" style="font-size:12pt;line-height:115%;color:rgb(17,85,204);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=3398</span></a><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><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%">Organizers: Giulio Iacobelli e Maria Eulalia Vares</span></p></div></div>
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