<div dir="ltr"><div><div>Aşağıda detayları verilen seminere ilgilenen herkes davetlidir.<br></div>saygılar<br></div>mesut<br clear="all"><div><div><div><div><div class="gmail_signature"><div dir="ltr">  <br><p class="MsoNormal" style="margin-bottom:0.0001pt;line-height:normal;background:white none repeat scroll 0% 0%"><b style><span style="font-size:14pt;font-family:"Times New Roman",serif;color:rgb(34,34,34)">Tarih (Date) :</span></b><span style="font-size:14pt;font-family:"Times New Roman",serif;color:rgb(34,34,34)"> 10.06.2015, Çarşamba
(</span><span style="font-size:14pt;font-family:"Times New Roman",serif;color:rgb(34,34,34)">Wednesday</span><span style="font-size:14pt;font-family:"Times New Roman",serif;color:rgb(34,34,34)">)<span style>                    </span></span></p>

<p class="MsoNormal" style="margin-bottom:0.0001pt;line-height:normal;background:white none repeat scroll 0% 0%"><b style><span style="font-size:14pt;font-family:"Times New Roman",serif;color:rgb(34,34,34)">Saat (Time):</span></b><span style="font-size:14pt;font-family:"Times New Roman",serif;color:rgb(34,34,34)"> 13:00</span></p>

<p class="MsoNormal" style="margin-bottom:0.0001pt;line-height:normal;background:white none repeat scroll 0% 0%"><b style><span style="font-size:14pt;font-family:"Times New Roman",serif;color:rgb(34,34,34)">Yer (Place):</span></b><span style="font-size:14pt;font-family:"Times New Roman",serif;color:rgb(34,34,34)"> Yaşar ATAMAN Seminer
Salonu</span></p>



<p class="MsoNormal" style="margin-bottom:12pt;line-height:normal"><b style><span style="font-size:14pt;font-family:"Times New Roman",serif;color:rgb(34,34,34)">Konuşmacı (Speaker):</span></b><span style="font-size:14pt;font-family:"Times New Roman",serif;color:rgb(34,34,34);background:white none repeat scroll 0% 0%">Dr. </span><span style="font-size:14pt;font-family:"Times",serif" lang="EN-US">Anargyros Katsampekis </span><span style="font-size:14pt;font-family:"Times New Roman",serif;color:rgb(34,34,34);background:white none repeat scroll 0% 0%">(</span><span style="font-size:12pt;font-family:"Times New Roman",serif">MSGSU</span><span style="font-size:14pt">)</span><span style="font-size:14pt;font-family:"Times New Roman",serif;color:rgb(34,34,34);background:white none repeat scroll 0% 0%"></span></p>

<p class="MsoNormal" style="margin-bottom:0.0001pt;line-height:normal"><b style><span style="font-size:14pt;font-family:"Times New Roman",serif;color:rgb(34,34,34)">Başlık (Title) :</span></b><span style="font-size:14pt;font-family:"Times New Roman",serif">Matching in graphs, circuits and
toric ideals</span></p>



<p class="MsoNormal" style="text-align:justify"><b style><span style="font-size:14pt;line-height:115%;font-family:"Times New Roman",serif;color:rgb(34,34,34)">Özet (Abstract) : </span></b><span style="font-size:14pt;line-height:115%;font-family:"Times New Roman",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. </span></p>

<p class="MsoNormal" style="text-align:justify;text-indent:35.4pt"><span style="font-size:14pt;line-height:115%;font-family:"Times New Roman",serif">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><span style="font-size:12pt;line-height:115%;font-family:"Times New Roman",serif"></span></p>

<p class="MsoNormal" style="margin-bottom:0.0001pt;text-align:justify;text-indent:35.4pt;line-height:normal"><span style="font-size:14pt;font-family:"Times New Roman",serif">In the talk we study the binomial arithmetical rank of
the toric ideal IG of a finite graph G in two cases: (1) G is bipartite, (2) IG
is generated by quadratic binomials. </span></p>

<p class="MsoNormal" style="margin-bottom:0.0001pt;text-align:justify;text-indent:35.4pt;line-height:normal"><span style="font-size:14pt;font-family:"Times New Roman",serif">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>

</p>

<p class="MsoNormal" style="margin-bottom:0.0001pt;line-height:normal;background:white none repeat scroll 0% 0%"><span style="font-size:14pt;font-family:"Times New Roman",serif;color:rgb(34,34,34)">NOT: Konuşma sonunda çay ve pasta ikramı olacaktır.</span></p>

<p class="MsoNormal" style="margin-bottom:0.0001pt;line-height:normal;background:white none repeat scroll 0% 0%"><span style="font-size:14pt;font-family:"Times New Roman",serif;color:rgb(34,34,34)">(P.S.<span style>  </span>Tea and </span><span style="font-size:14pt;font-family:"Times New Roman",serif">cookies will be
served after the talk</span><span style="font-size:14pt;font-family:"Times New Roman",serif;color:rgb(34,34,34)">.)</span></p><br>  Mesut Sahin<div>  Associate Professor<br>  Department of Mathematics<br>  Hacettepe University<br>  TR 06800 Beytepe </div><div>  ANKARA - TURKEY<br> <a href="http://yunus.hacettepe.edu.tr/~mesut.sahin" target="_blank">http://yunus.hacettepe.edu.tr/~mesut.sahin</a></div></div></div></div>
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