<div dir="ltr"><br clear="all"><div><div class="gmail_signature"><p class="MsoNormal" style="margin-bottom:0.0001pt;background-image:initial;background-repeat:initial"><span style="font-size:10pt;font-family:Tahoma,sans-serif">Sayın liste üyeleri,</span></p>

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<p class="MsoNormal"><span style="font-size:10pt;line-height:115%;font-family:Tahoma,sans-serif">İzmir Ekonomi Üniversitesi, Matematik Bölümü
tarafından düzenlenen Matematik-İstatistik
seminerleri kapsamında,  Dr.</span><span style="font-size:10pt;line-height:115%;font-family:Tahoma,sans-serif;background-image:initial;background-repeat:initial"> Anargyros Katsampekis</span><span style="font-size:10pt;line-height:115%;font-family:Tahoma,sans-serif"> tarafından 27 Mayıs 2015,
saat 14.00'de, M201 nolu sınıfta  “</span><span style="font-size:10pt;line-height:115%;font-family:Tahoma,sans-serif;background-image:initial;background-repeat:initial">Matching in graphs, circuits and toric ideals</span><span style="font-size:10pt;line-height:115%;font-family:Tahoma,sans-serif;background-image:initial;background-repeat:initial">”  </span><span style="font-size:10pt;line-height:115%;font-family:Tahoma,sans-serif">başlıklı bir seminer verilecektir.</span><span style="font-size:10pt;line-height:115%;font-family:Tahoma,sans-serif;background-image:initial;background-repeat:initial"></span></p><p class="MsoNormal"><span style="font-size:10pt;line-height:115%;font-family:Tahoma,sans-serif"><br></span></p>

<p class="MsoNormal" style="background-image:initial;background-repeat:initial"><span style="font-size:10pt;font-family:Tahoma,sans-serif">Seminerin detayları aşağıda belirtilmiş olup tüm
ilgilenenler davetlidir.</span></p>

<p class="MsoNormal" style="margin-bottom:12pt;background-image:initial;background-repeat:initial"><span style="font-size:10pt;font-family:Tahoma,sans-serif">İyi çalışmalar.<br>
<br>
Burcu Silindir Yantır</span></p>

<p class="MsoNormal" style="margin-bottom:12pt;background-image:initial;background-repeat:initial"><span style="font-size:10pt;font-family:Tahoma,sans-serif">İzmir Ekonomi Üniversitesi</span></p>

<p class="MsoNormal" style="margin-bottom:12pt;background-image:initial;background-repeat:initial"><span style="font-size:10pt;font-family:Tahoma,sans-serif">Matematik Bölümü<br>
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<p class="MsoNormal"><span style="font-size:10pt;line-height:115%;font-family:Tahoma,sans-serif">Dear all,<br>
<br>
İzmir University of Economics, Department of Mathematics continues its
Mathematics-Statistics seminars on May 27 th, 2015, at 14.00 pm at M201, with Dr.</span><span style="font-size:10pt;line-height:115%;font-family:Tahoma,sans-serif;background-image:initial;background-repeat:initial"> Anargyros Katsampekis</span>.<span style="font-size:10pt;line-height:115%;font-family:Tahoma,sans-serif"> His  talk is entitled as<span style="background-image:initial;background-repeat:initial"> “</span></span><span style="font-size:10pt;line-height:115%;font-family:Tahoma,sans-serif;background-image:initial;background-repeat:initial">Matching in graphs, circuits and toric ideals</span><span style="font-size:10pt;line-height:115%;font-family:Tahoma,sans-serif">”</span><span style="font-size:10pt;line-height:115%;font-family:Tahoma,sans-serif;background-image:initial;background-repeat:initial">.</span><span style="font-size:10pt;line-height:115%;font-family:Tahoma,sans-serif;background-image:initial;background-repeat:initial"></span></p><p class="MsoNormal"><span style="font-size:10pt;line-height:115%;font-family:Tahoma,sans-serif;background-image:initial;background-repeat:initial"><br></span></p>

<p class="MsoNormal"><span style="font-size:10pt;font-family:Tahoma,sans-serif"> All are most welcome to attend.</span><span style="font-size:10pt;font-family:Tahoma,sans-serif;background-image:initial;background-repeat:initial"> </span><span style="font-size:10pt;font-family:Tahoma,sans-serif"></span></p>

<p class="MsoNormal" style="margin-bottom:0.0001pt;background-image:initial;background-repeat:initial"><span style="font-size:10pt;font-family:Tahoma,sans-serif"> </span></p>

<p class="MsoNormal" style="margin-bottom:0.0001pt;background-image:initial;background-repeat:initial"><span style="font-size:10pt;font-family:Tahoma,sans-serif">Please find the  more detailed
announcement below.<br>
<br>
Sincerely</span></p>

<p class="MsoNormal" style="margin-bottom:0.0001pt;background-image:initial;background-repeat:initial"><span style="font-size:10pt;font-family:Tahoma,sans-serif">Burcu Silindir Yantır<br>
İzmir University of Economics</span></p>

<p class="MsoNormal" style="margin-bottom:0.0001pt;background-image:initial;background-repeat:initial"><span style="font-size:10pt;font-family:Tahoma,sans-serif">Department of Mathematics</span></p>

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<p class="MsoNormal"><b><span style="font-size:10pt;line-height:115%;font-family:Tahoma,sans-serif">Abstract:</span></b><span style="font-size:10pt;line-height:115%;font-family:Tahoma,sans-serif"> </span><span style="font-size:10pt;line-height:115%;font-family:Tahoma,sans-serif">Toric ideals are binomial
ideals which represent the algebraic relations of finite sets of power
products. They have applications in diverse areas in mathematics, such as
algebraic statistics, integer programming, hypergeometric differential
equations, graph theory, etc. A basic problem in Commutative Algebra asks one
to compute the least number of polynomials needed to generate the toric ideal
up to radical. This number is commonly known as the arithmetical rank of a
toric ideal. A usual approach to this problem is to restrict to a certain class
of polynomials and ask how many polynomials from this class can generate the
toric ideal up to radical. Restricting the polynomials to the class of
binomials we arrive at the notion of the binomial arithmetical rank of a toric
ideal. </span></p>

<p class="MsoNormal"><span style="font-size:10pt;line-height:115%;font-family:Tahoma,sans-serif">In the talk we study the binomial arithmetical rank of
the toric ideal IG of a finite graph G in two cases: </span></p>

<p class="MsoNormal"><span style="font-size:10pt;line-height:115%;font-family:Tahoma,sans-serif">(1) G is bipartite, </span></p>

<p class="MsoNormal"><span style="font-size:10pt;line-height:115%;font-family:Tahoma,sans-serif">(2) IG is generated by quadratic binomials. Using a
generalized notion of a matching in a graph and circuits of toric ideals, we
prove that, in both cases, the binomial arithmetical rank equals the minimal
number of generators of IG.</span><span style="font-size:10pt;line-height:115%;font-family:Tahoma,sans-serif"></span></p></div></div>
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