<html><head><meta http-equiv="Content-Type" content="text/html charset=utf-8"><meta http-equiv="Content-Type" content="text/html charset=utf-8"></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space;" class=""><div class="" style="font-family: LucidaGrande;"><span class=""><b class="">REMINDER:</b></span></div><span class="" style="font-family: LucidaGrande;"><div class=""><span class=""><br class=""></span></div>Departments of Computer Science & Mathematics</span><div class="" style="font-family: LucidaGrande;">Combinatorics & Theoretical Seminar</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 style="font-family: LucidaGrande; text-align: -webkit-auto;" class=""><br class=""></div><div style="text-align: -webkit-auto;" class=""><div style="font-family: 'Lucida Grande'; text-align: -webkit-auto;" class=""><font face="Times New Roman" class="">Today, Tuesday, September 13, 2016</font></div><div style="font-family: 'Lucida Grande'; text-align: -webkit-auto;" class=""><font face="Times New Roman" class="">3:00 pm</font></div><div style="font-family: 'Lucida Grande'; text-align: -webkit-auto;" class=""><font face="Times New Roman" class="">Ryerson 251</font></div><div style="font-family: 'Lucida Grande';" class=""><font face="Times New Roman" class=""><br class=""></font></div><div style="font-family: 'Lucida Grande';" class=""><font face="Times New Roman" class=""><b class="">Annie Raymond</b></font></div><div style="font-family: 'Lucida Grande';" class=""><font face="Times New Roman" class=""><b class="">University of Washington</b></font></div><div class=""><p class="MsoNormal" style="font-family: 'Lucida Grande';"><font face="Times New Roman" class="">Title: “Siegel's Theorem, Edge Coloring, and a Holant Dichotomy”</font></p><div class="">
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<!--StartFragment--><p class="MsoNormal" style="text-align: justify;"><font face="Times New Roman" class="">Abstract: What do
Siegel’s theorem on finiteness of integer solutions have to do
with complexity theory? In this talk we discuss a new complexity
dichotomy theorem for counting problems. Such a dichotomy is a
classification of a class of problems into exactly two kinds:
those that are polynomial time computable, and those that are #P-hard,
and thus intractable. (For logicians, a complexity dichotomy theorem
is a kind of restricted anti-Friedberg-Muchnick Theorem.) An example
problem in this dichotomy is the problem of counting the number
of valid edge colorings of a graph. We will show that an effective
version of Siegel’s theorem and some Galois theory are key
ingredients in the proof of this dichotomy. Along the way we will
also meet the Tutte polynomial, medial graphs, Eulerian orientations,
Puiseux series, and a certain lattice condition on the (logarithms
of) the roots of polynomials with integer coefficients.</font><span style="font-family: 'Times New Roman'; text-align: -webkit-auto;" class="">Joint
work with Heng Guo and Tyson Williams.</span></p><p class="MsoNormal"><span style="font-family: 'Times New Roman'; text-align: -webkit-auto;" class="">Host: Prof.
Alexander Razborov</span></p><p class="MsoNormal"><font face="Times New Roman" class="">*Refreshments will
be served prior to the talk in Ryerson 255 @ 2:30 pm*</font><o:p class=""></o:p></p>
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