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<p class="MsoNormal" style="line-height:115%;font-size:11pt;font-family:"Calibri","sans-serif""><b><span style="font-size:12pt;line-height:115%" lang="EN-US">Probability Webinar -<span> </span>IM-UFRJ <span></span></span></b></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%" lang="EN-US"><span> </span></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%" lang="EN-US">Dear colleagues,<span>
</span><span></span></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%" lang="EN-US">Our next online seminar will be held on Monday, <b>April 12</b>, from <b>3 p.m. to 4 p.m</b>.
(Rio de Janeiro local time)<span></span></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%" lang="EN-US">The GoogleMeet link for the seminar is </span><a href="https://meet.google.com/uew-ehhn-kby" style="color:blue;text-decoration:underline" target="_blank"><span style="font-size:12pt;line-height:115%" lang="EN-US">https://meet.google.com/uew-ehhn-kby</span></a><span style="font-size:12pt;line-height:115%" lang="EN-US">
<span></span></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%" lang="EN-US"><span> </span></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%" lang="EN-US">Speaker:<span> </span><b><span style="font-family:"Calibri","sans-serif"">Yuval Peres </span></b></span><b><span style="font-size:12pt;line-height:115%;font-family:"Calibri","sans-serif"" lang="ES-AR">(</span></b><b><span style="font-size:12pt;line-height:115%" lang="ES-AR">Kent
State University</span></b><b><span style="font-size:12pt;line-height:115%;font-family:"Calibri","sans-serif"" lang="EN-US">)</span></b><b><span style="font-size:12pt;line-height:115%" lang="EN-US"><span></span></span></b></p>
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<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%" lang="EN-US">Title:
</span><b><span style="font-size:12pt;line-height:115%" lang="EN-US">Gravitational
allocation of uniform points on the sphere<span></span></span></b></p>
<p class="MsoNormal" style="line-height:115%;font-size:11pt;font-family:"Calibri","sans-serif""><span style="font-size:12pt;line-height:115%" lang="EN-US">Abstract: </span><span style="font-size:12pt;line-height:115%" lang="EN-US">Given uniform points on the
surface of a two-dimensional sphere, how can we partition the sphere fairly
among them? "Fairly" means that each region has the same area. It
turns out that if the given points apply a two-dimensional gravity force to the
rest of the sphere, then the basins of attraction for the resulting gradient
flow yield such a partition-with exactly equal areas, no matter how the points
are distributed. This is related to work of Nazarov-Sodin-Volberg on Gaussian
analytic functions. (See the cover of the AMS Notices at </span><a href="http://www.ams.org/publications/journals/notices/201705/rnoti-cvr1.pdf" style="color:blue;text-decoration:underline" target="_blank"><span style="font-size:12pt;line-height:115%" lang="EN-US">http://www.ams.org/publications/journals/notices/201705/rnoti-cvr1.pdf</span></a><span style="font-size:12pt;line-height:115%" lang="EN-US">.) Our
main result is that this partition minimizes, up to a bounded factor, the
average distance between points in the same cell. I will also present an
application to almost optimal matching on the sphere, connecting to a classical
result of Ajtai, Komlos and Tusnady (Combinatorica 1984). <span></span></span></p>
<p class="MsoNormal" style="line-height:115%;font-size:11pt;font-family:"Calibri","sans-serif""><span style="font-size:12pt;line-height:115%" lang="EN-US">Joint work with Nina Holden
and Alex Zhai.<b><span></span></b></span></p>
<p class="MsoNormal" style="line-height:115%;font-size:11pt;font-family:"Calibri","sans-serif""><span style="font-size:12pt;line-height:115%" lang="EN-US"><span> </span></span></p>
<p class="MsoNormal" style="line-height:115%;font-size:11pt;font-family:"Calibri","sans-serif""><span style="font-size:12pt;line-height:115%" lang="EN-US">All the talks
are held in English. <span></span></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%" lang="EN-US">The videos of the online seminars held in 2020 are
available at <a href="http://www.dme.ufrj.br/?page_id=2885" target="_blank">http://www.dme.ufrj.br/?page_id=2885</a><span></span></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%" lang="EN-US">For the 2021 series, a few days after each meeting the
video should be available at <a href="http://www.dme.ufrj.br/?page_id=3027" target="_blank">http://www.dme.ufrj.br/?page_id=3027</a><span></span></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%" lang="EN-US"><span> </span></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%" lang="EN-US">Thanks for circulating this information. <span></span></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%" lang="EN-US">Sincerely, <br>
Organizers: Guilherme Ost and Maria Eulalia Vares<span></span></span></p>
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