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<p><font style="font-family:Arial,Helvetica,sans-serif" size="3" color="black"><span dir="ltr" style="font-size:12pt; background-color:white">Dear all,<br>
<br>
On Thursday 24 November <span style="white-space:nowrap">Zafeirakis Zafeirakopoulos</span> (Gebze Technical University) will give a talk in the Bilkent Algebra seminar.<br>
The title of his talk is<br>
        "</span></font><font style="font-family: Arial,Helvetica,sans-serif; font-size: 12pt;" size="3" color="black"><span dir="ltr" style="background-color: white;"><span dir="ltr" style="">Polyhedral Omega: Solving linear Diophantine systems</span><span style="white-space:nowrap"><font size="2"><span style="font-size:10pt"></span></font></span>".<br>
<br>
Abstract:<br>
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<font style="font-family: Arial,Helvetica,sans-serif;" color="black"><span dir="ltr" style="background-color: white;"><span dir="ltr" style=""><span style="background-color: white;">Polyhedral</span> <span style="background-color: white;">Omega</span> is a
 new algorithm for solving linear Diophantine systems (LDS), i.e., for computing a multivariate rational function representation of the set of all non-negative integer solutions to a system of linear equations and inequalities.
<span style="background-color: white;">Polyhedral</span><span style="background-color: white;"> Omega</span> combines methods from partition analysis with methods from <span style="background-color: white;">polyhedral</span> geometry. In particular, we combine
 MacMahon’s iterative approach based on the <span style="background-color: white;">Omega</span> operator and explicit formulas for its evaluation with geometric tools such as Brion decomposition and Barvinok’s short rational function representations. This synthesis
 of ideas makes <span style="background-color: white;">Polyhedral</span> <span style="background-color: white;">Omega</span> by far the simplest algorithm for solving linear Diophantine systems available to date.</span><br>
<br>
  <br>
Time: 11.00,<br>
Place: Mathematics Department Seminar Room SA-141.<br>
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Best regards,<br>
<br>
Anargyros Katsampekis</span></font> </span></div>
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