<html><head><meta http-equiv="content-type" content="text/html; charset=utf-8"></head><body dir="auto"><div class=""><span class="" style="background-color: rgba(255, 255, 255, 0);"><b class="">REMINDER:</b></span></div><span class="" style="background-color: rgba(255, 255, 255, 0);"><div class=""><span class=""><br class=""></span></div>Departments of Computer Science & Mathematics</span><div class=""><span style="background-color: rgba(255, 255, 255, 0);">Combinatorics & Theoretical Seminar</span></div><div apple-content-edited="true" class=""><div class="" style="orphans: 2; text-align: -webkit-auto; widows: 2; word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space;"><div class="" style="text-align: -webkit-auto; word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space;"><div class="" style="text-align: -webkit-auto; word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space;"><div class="" style="text-align: -webkit-auto;"><div class="" style="orphans: auto; widows: auto;"><span style="background-color: rgba(255, 255, 255, 0);"><br class=""></span></div><div class="" style="text-align: -webkit-auto;"><div class="" style="orphans: auto; widows: auto;"><font class="" style="background-color: rgba(255, 255, 255, 0);">Today, Tuesday, September 13, 2016</font></div><div class="" style="orphans: auto; widows: auto;"><font class=""><a dir="ltr" href="x-apple-data-detectors://2" x-apple-data-detectors="true" x-apple-data-detectors-type="calendar-event" x-apple-data-detectors-result="2" style="background-color: rgba(255, 255, 255, 0);">3:00 pm</a></font></div><div class="" style="orphans: auto; widows: auto;"><font class="" style="background-color: rgba(255, 255, 255, 0);">Ryerson 251</font></div><div class="" style="orphans: auto; widows: auto;"><font class="" style="background-color: rgba(255, 255, 255, 0);"><br class=""></font></div><div class="" style="orphans: auto; widows: auto;"><font class=""><b class="" style="background-color: rgba(255, 255, 255, 0);">Annie Raymond</b></font></div><div class="" style="orphans: auto; widows: auto;"><font class=""><b class="" style="background-color: rgba(255, 255, 255, 0);">University of Washington</b></font></div><div class=""><p class="MsoNormal" style="orphans: auto; widows: auto;"><font class="" style="background-color: rgba(255, 255, 255, 0);">Title: “Symmetric Sums of Squares over $k$-Subset Hypercubes”</font></p><div class=""><p class="MsoNormal" style="orphans: auto; text-align: start; widows: auto;"><span style="background-color: rgba(255, 255, 255, 0);"><font class="">Abstract: </font></span><span style="text-align: -webkit-auto; orphans: 2; widows: 2;">We consider the problem of finding sum of squares (sos) expressions to establish the non-negativity of a symmetric polynomial over a discrete hypercube whose coordinates are indexed by $k$-element subsets of $[n]$. We develop a variant of the Gatermann-Parrilo symmetry-reduction method tailored to our setting that allows for several simplifications and a connection to Razborov's flag algebras. We show that every symmetric polynomial that has a sos expression of a fixed degree also has a succinct sos expression whose size depends only on the degree and not on the number of variables. This is joint work with James Saunderson, Mohit Singh and Rekha Thomas. </span></p><p class="MsoNormal" style="orphans: auto; widows: auto;"><span class="" style="text-align: -webkit-auto; background-color: rgba(255, 255, 255, 0);">Host: Prof. Alexander Razborov</span></p><p class="MsoNormal" style="orphans: auto; widows: auto;"><span style="background-color: rgba(255, 255, 255, 0);"><font class="">*Refreshments will be served prior to the talk in Ryerson 255 <a dir="ltr" href="x-apple-data-detectors://5" x-apple-data-detectors="true" x-apple-data-detectors-type="calendar-event" x-apple-data-detectors-result="5">@ 2:30</a> pm*</font><o:p class=""></o:p></span></p></div></div></div></div></div></div></div></div><span style="background-color: rgba(255, 255, 255, 0);">_______________________________________________<br>Colloquium mailing list - <a dir="ltr" href="mailto:Colloquium@mailman.cs.uchicago.edu" x-apple-data-detectors="true" x-apple-data-detectors-type="link" x-apple-data-detectors-result="6">Colloquium@mailman.cs.uchicago.edu</a><br><a dir="ltr" href="https://mailman.cs.uchicago.edu/mailman/listinfo/colloquium" x-apple-data-detectors="true" x-apple-data-detectors-type="link" x-apple-data-detectors-result="7">https://mailman.cs.uchicago.edu/mailman/listinfo/colloquium</a><br>_______________________________________________<br>faculty mailing list - <a dir="ltr" href="mailto:faculty@mailman.cs.uchicago.edu" x-apple-data-detectors="true" x-apple-data-detectors-type="link" x-apple-data-detectors-result="8">faculty@mailman.cs.uchicago.edu</a><br><a dir="ltr" href="https://mailman.cs.uchicago.edu/mailman/listinfo/faculty" x-apple-data-detectors="true" x-apple-data-detectors-type="link" x-apple-data-detectors-result="9">https://mailman.cs.uchicago.edu/mailman/listinfo/faculty</a></span><div></div></body></html>