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<p style="font-family: Calibri, Arial, Helvetica, sans-serif; font-size: 16px;">Dear all,<br>
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<p style="font-family: Calibri, Arial, Helvetica, sans-serif; font-size: 16px;"><br>
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<p style="font-family: Calibri, Arial, Helvetica, sans-serif; font-size: 16px;">The Ankara-Istanbul Commutative Algebra Workshop 3 will take place in Ankara, </p>
<p style="font-family: Calibri, Arial, Helvetica, sans-serif; font-size: 16px;">at Hacettepe University, on 19 December 2015. </p>
<p style="font-family: Calibri, Arial, Helvetica, sans-serif; font-size: 16px;">The speakers are Mufit Sezer (Bilkent University) and </p>
<p style="font-family: Calibri, Arial, Helvetica, sans-serif; font-size: 16px;">Marius Vladoiu (Bucharest University). <br>
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<p style="font-family: Calibri, Arial, Helvetica, sans-serif; font-size: 16px;"><br>
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<p style="font-family: Calibri, Arial, Helvetica, sans-serif; font-size: 16px;">The program is as follows:</p>
<p style="font-family: Calibri, Arial, Helvetica, sans-serif; font-size: 16px;"><span style="font-family: Calibri, Arial, Helvetica, sans-serif; font-size: 16px; background-color: rgb(255, 255, 255);">11.00-12.00</span> Mufit Sezer,
<span style="color: rgb(33, 33, 33); line-height: normal; font-family: Calibri, Arial, Helvetica, sans-serif; background-color: transparent;">
<span style="font-family: Calibri, Arial, Helvetica, sans-serif;">On Cohen-Macaulayness and depth of ideals in invariant rings</span></span>.</p>
<p style="font-family: Calibri, Arial, Helvetica, sans-serif; font-size: 16px;">12.00-13.00 Lunch break.</p>
<p style="font-family: Calibri, Arial, Helvetica, sans-serif; font-size: 16px;">13.00-14.00 Marius Vladoiu,
<span style="font-family: Calibri, Arial, Helvetica, sans-serif; font-size: 12pt; background-color: rgb(255, 255, 255);">
<span style="font-family: Calibri, Arial, Helvetica, sans-serif;">Combinatorial classification of toric ideals and applications</span></span>.<br>
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<p style="font-family: Calibri, Arial, Helvetica, sans-serif; font-size: 16px;"><br>
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<div style="color: rgb(68, 68, 68); font-size: 13.3333px; line-height: 21.3333px; background-color: rgb(255, 255, 255);">
<font size="3" style="font-family: Calibri, Arial, Helvetica, sans-serif;"><span style="font-family: Calibri, Arial, Helvetica, sans-serif;">Abstracts of the talks.</span></font></div>
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<font size="3" style="font-family: Calibri, Arial, Helvetica, sans-serif;"><br style="font-family: Calibri, Arial, Helvetica, sans-serif;">
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<font size="3" style="font-family: Calibri, Arial, Helvetica, sans-serif;"><span style="font-family: Calibri, Arial, Helvetica, sans-serif;">(1) Mufit Sezer. </span></font><span style="font-size: medium; color: rgb(33, 33, 33); line-height: normal; font-family: Calibri, Arial, Helvetica, sans-serif; background-color: transparent;"><span style="font-family: Calibri, Arial, Helvetica, sans-serif;">On
Cohen-Macaulayness and depth of ideals in invariant rings</span></span><span style="font-size: medium; line-height: 25.6px; font-family: Calibri, Arial, Helvetica, sans-serif; background-color: transparent;"><span style="font-family: Calibri, Arial, Helvetica, sans-serif;">.</span></span></div>
<div style="color: rgb(68, 68, 68); font-size: 13.3333px; line-height: 21.3333px; background-color: rgb(255, 255, 255);">
<font size="3" style="font-family: Calibri, Arial, Helvetica, sans-serif;"><span style="color: rgb(33, 33, 33); line-height: normal; font-family: Calibri, Arial, Helvetica, sans-serif;"><span style="font-family: Calibri, Arial, Helvetica, sans-serif;">We investigate
the presence of Cohen-Macaulay ideals in invariant</span></span><br style="color: rgb(33, 33, 33); line-height: normal; font-family: Calibri, Arial, Helvetica, sans-serif;">
<span style="color: rgb(33, 33, 33); line-height: normal; font-family: Calibri, Arial, Helvetica, sans-serif;"><span style="font-family: Calibri, Arial, Helvetica, sans-serif;">rings and show that an ideal of an invariant ring corresponding</span></span><br style="color: rgb(33, 33, 33); line-height: normal; font-family: Calibri, Arial, Helvetica, sans-serif;">
<span style="color: rgb(33, 33, 33); line-height: normal; font-family: Calibri, Arial, Helvetica, sans-serif;"><span style="font-family: Calibri, Arial, Helvetica, sans-serif;">to a modular representation of a p-group is not Cohen-Macaulay</span></span><br style="color: rgb(33, 33, 33); line-height: normal; font-family: Calibri, Arial, Helvetica, sans-serif;">
<span style="color: rgb(33, 33, 33); line-height: normal; font-family: Calibri, Arial, Helvetica, sans-serif;"><span style="font-family: Calibri, Arial, Helvetica, sans-serif;">unless the invariant ring itself is. For modular cyclic groups of prime</span></span><br style="color: rgb(33, 33, 33); line-height: normal; font-family: Calibri, Arial, Helvetica, sans-serif;">
<span style="color: rgb(33, 33, 33); line-height: normal; font-family: Calibri, Arial, Helvetica, sans-serif;"><span style="font-family: Calibri, Arial, Helvetica, sans-serif;">order, we show that the quotient of the invariant ring modulo the transfer</span></span><br style="color: rgb(33, 33, 33); line-height: normal; font-family: Calibri, Arial, Helvetica, sans-serif;">
<span style="color: rgb(33, 33, 33); line-height: normal; font-family: Calibri, Arial, Helvetica, sans-serif;"><span style="font-family: Calibri, Arial, Helvetica, sans-serif;">ideal is </span></span><span style="color: rgb(33, 33, 33); line-height: normal; font-family: Calibri, Arial, Helvetica, sans-serif;"><span style="font-family: Calibri, Arial, Helvetica, sans-serif;">always
Cohen-Macaulay. This is joint with M. Kohls.</span></span></font></div>
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<font size="3" style="font-family: Calibri, Arial, Helvetica, sans-serif;"><br style="font-family: Calibri, Arial, Helvetica, sans-serif;">
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<span style="font-size: medium; color: rgb(0, 0, 0); line-height: normal; font-family: Calibri, Arial, Helvetica, sans-serif; background-color: transparent;"><span style="font-family: Calibri, Arial, Helvetica, sans-serif;">(2) Marius Vladoiu. Combinatorial
classification of toric ideals and applications.</span></span></div>
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<div style="color: rgb(0, 0, 0); line-height: normal;"><font size="3" style="font-family: Calibri, Arial, Helvetica, sans-serif;"><span style="font-family: Calibri, Arial, Helvetica, sans-serif;">We discuss a combinatorial classification of all toric ideals
based on the bouquet structure </span></font></div>
<div style="color: rgb(0, 0, 0); line-height: normal;"><font size="3" style="font-family: Calibri, Arial, Helvetica, sans-serif;"><span style="font-family: Calibri, Arial, Helvetica, sans-serif;">we introduce in a joint work with Sonja Petrovic and Apostolos
Thoma. On one end of the spectrum of this </span></font></div>
<div style="color: rgb(0, 0, 0); line-height: normal;"><font size="3" style="font-family: Calibri, Arial, Helvetica, sans-serif;"><span style="font-family: Calibri, Arial, Helvetica, sans-serif;">classification there are ideals, that we call stable, for which
bouquets capture the complexity of various generating sets </span></font></div>
<div style="color: rgb(0, 0, 0); line-height: normal;"><font size="3" style="font-family: Calibri, Arial, Helvetica, sans-serif;"><span style="font-family: Calibri, Arial, Helvetica, sans-serif;">and the minimal graded free resolution, while on the other end
of the spectrum of this classification lie toric ideals whose </span></font></div>
<div style="color: rgb(0, 0, 0); line-height: normal;"><font size="3" style="font-family: Calibri, Arial, Helvetica, sans-serif;"><span style="font-family: Calibri, Arial, Helvetica, sans-serif;">various bases (e.g. indispensable and Graver) coincide. We discuss
several applications of this classification, the main ones </span></font></div>
<div style="color: rgb(0, 0, 0); line-height: normal;"><font size="3" style="font-family: Calibri, Arial, Helvetica, sans-serif;"><span style="font-family: Calibri, Arial, Helvetica, sans-serif;">being the solution of an open problem in combinatorial commutative
algebra, and that all positively graded toric ideals are encoded by </span></font></div>
<div style="color: rgb(0, 0, 0); line-height: normal;"><font size="3" style="font-family: Calibri, Arial, Helvetica, sans-serif;"><span style="font-family: Calibri, Arial, Helvetica, sans-serif;">toric ideals of hypergraphs, i.e. toric ideals of 0-1 matrices. </span></font></div>
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<p style="font-family: Calibri, Arial, Helvetica, sans-serif; font-size: 16px;"> </p>
<p style="font-family: Calibri, Arial, Helvetica, sans-serif; font-size: 16px;">The workshop will be held in Class 24.<br>
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<p style="font-family: Calibri, Arial, Helvetica, sans-serif; font-size: 16px;"><br>
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<p style="font-family: Calibri, Arial, Helvetica, sans-serif; font-size: 16px;">I also maintain the webpage: <a href="https://sites.google.com/site/katsabekmath/ankara-istanbul-commalg">https://sites.google.com/site/katsabekmath/ankara-istanbul-commalg</a><br>
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<p style="font-family: Calibri, Arial, Helvetica, sans-serif; font-size: 16px;"> </p>
<p style="font-family: Calibri, Arial, Helvetica, sans-serif; font-size: 16px;">Everyone is welcome.<br>
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<p style="font-family: Calibri, Arial, Helvetica, sans-serif; font-size: 16px;">Best regards,<br>
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<p style="font-family: Calibri, Arial, Helvetica, sans-serif; font-size: 16px;">Anargyros Katsampekis<br>
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