<div dir="ltr"><div class="gmail_default" style="font-family:arial,helvetica,sans-serif">Dear All,</div><div class="gmail_default" style="font-family:arial,helvetica,sans-serif"><br></div><div class="gmail_default" style="font-family:arial,helvetica,sans-serif">Dr. Anargyros Katsampekis from MSGSU will hold a seminar at Sabancı University on "<strong>A combinatorial approach for determining the binomial arithmetical rank of a toric ideal</strong>" on Tuesday, November 17 at 15:45, in FENS 2008. </div><div><br></div><div>All interested are welcome to attend. For directions to Sabancı University please visit:<br></div><div><br></div><div><a href="http://www.sabanciuniv.edu/en/transportation/shuttle-hours" target="_blank">http://www.sabanciuniv.edu/en/transportation/shuttle-hours</a></div><div><br></div><div><strong>Abstarct: </strong></div><div><font color="#000000" face="Times New Roman"></font><p style="margin:5pt 0in;text-align:justify;line-height:normal"><font color="#000000"><span style="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, codingtheory, hypergeometric differential equations, graph theory, etc.</span><span style="font-family:"cmr10","sans-serif""> </span><span style="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. In the talk we study the binomial arithmetical rank of the toric ideal </span><i><span style="font-family:cmmi10">I</span></i><i><span style="font-family:cmmi8">G</span></i><span style="font-family:"Times New Roman","serif"">  of a finite graph <i>G </i>in two cases:</span></font></p><font color="#000000" face="Times New Roman"></font><p style="margin:5pt 0in;text-align:justify;line-height:normal"><span style="font-family:"Times New Roman","serif""><font color="#000000">(1) G is bipartite,</font></span></p><font color="#000000" face="Times New Roman"></font><p style="margin:5pt 0in;text-align:justify;line-height:normal"><font color="#000000"><span style="font-family:"Times New Roman","serif"">(2)  </span><i><span style="font-family:cmmi10">I</span></i><i><span style="font-family:cmmi8">G</span></i><span style="font-family:"Times New Roman","serif"">  is generated by quadratic polynomials.</span></font></p><font color="#000000" face="Times New Roman"></font><p style="margin:5pt 0in;text-align:justify;line-height:normal"><font color="#000000"><span style="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 </span><i><span style="font-family:cmmi10">I</span></i><i><span style="font-family:cmmi8">G</span></i><span style="font-family:"Times New Roman","serif"">.</span></font></p><p style="margin:5pt 0in;text-align:justify;line-height:normal"><font color="#000000"><span style="font-family:"Times New Roman","serif"">greetings</span></font></p><p style="margin:5pt 0in;text-align:justify;line-height:normal"><font color="#000000"><span style="font-family:"Times New Roman","serif"">canan kaşıkcı<br></span></font></p><p style="margin:5pt 0in;text-align:justify;line-height:normal"><font color="#000000"><span style="font-family:"Times New Roman","serif""><br></span></font></p><p style="margin:5pt 0in;text-align:justify;line-height:normal"><font color="#000000"><span style="font-family:"Times New Roman","serif""><br></span></font></p><p style="margin:5pt 0in;text-align:justify;line-height:normal"><font color="#000000"><span style="font-family:"Times New Roman","serif""><br></span></font></p><p style="margin:5pt 0in;text-align:justify;line-height:normal"><font color="#000000"><span style="font-family:"Times New Roman","serif""><br></span></font></p><p style="margin:5pt 0in;text-align:justify;line-height:normal"><font color="#000000"><span style="font-family:"Times New Roman","serif""><br></span></font></p><p style="margin:5pt 0in;text-align:justify;line-height:normal"><font color="#000000"><span style="font-family:"Times New Roman","serif""><br></span></font></p></div></div>