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<div align="center"><big><b><big>Welcome to the 2026
Spring talks of ODTÜ-Bilkent Algebraic Geometry
Seminars</big></b></big><b><br>
</b></div>
<div align="center"><i>since 2000</i><br>
</div>
<div align="center"><b><b>=================================================================</b></b><br>
<br>
This week the <a
href="http://www.bilkent.edu.tr/~sertoz/agseminar.htm"
target="_blank" moz-do-not-send="true">ODTÜ-Bilkent
Algebraic Geometry Seminar</a> is <b>online</b><br>
<br>
<i><font color="#ff00ff">This talk will begin at <u><b>15:40</b></u><u> (GMT+3)</u></font></i><br>
<a
href="https://www.timeanddate.com/worldclock/fixedtime.html?msg=ODT%C3%9C-Bilkent+Algebraic+Geometry+Seminar&iso=20260327T1540&p1=19&ah=1"
target="_blank" moz-do-not-send="true">Please check
your time difference between Ankara and your city here</a><br>
<b>=================================================================<br>
<br>
</b></div>
<div align="center">
<div align="center"><img
src="cid:part1.KbUACtLI.c88yvoFU@bilkent.edu.tr"
alt="" width="451" height="558" class=""></div>
</div>
<div align="center"><br>
</div>
<div align="center"><i>Ben Viegers (1886-1947)<br>
</i></div>
<div align="center"><i><br>
</i></div>
<div align="center"><i><br>
</i>
<div align="left">
<div align="left"><b><b moz-do-not-send="true"
href="https://fens.sabanciuniv.edu/tr/faculty-members/detail/3419"><font
color="#ff0000">Speaker: </font> <a
moz-do-not-send="true"
href="https://avesis.hacettepe.edu.tr/mesut.sahin">Mesut Şahin</a></b></b></div>
<b><b><font color="#ff0000"><font color="#000000"> </font></font></b></b><b><b><font
color="#ff0000">Affiliation: </font><i>Hacettepe<br>
<br>
</i></b></b></div>
<div align="left"><b><b><font color="#ff0000"> Title:<font
color="#000000"> Grobner Bases and Linear
Codes on Weighted Projective Planes<br>
</font></font></b></b></div>
</div>
<div align="justify"><b><b><font color="#ff0000">Abstract:</font></b></b>
Let $F$ be the finite field with $q$ elements and $K$
be its algebraic closure. The ring $S=F[x_0,x_1,x_2]$ is
graded via $\deg(x_i)=w_i$, for $i=0,1,2$, where $w_0,
w_1$ and $w_2$ generate a numerical semigroup! We study
some linear codes obtained from the weighted projective
plane $P(w_0,w_1,w_2)$ over $K$.<br>
<br>
We get a linear code by evaluating homogeneous
polynomials of degree $d$ at the subset $Y\{
P_1,...,P_N\}$ of $F$-rational points, which defines the
evaluation map: $f \mapsto (f(P_1),...f(P_N))$. The
image is a subspace of $F^N$, which is called a weighted
projective Reed-Muller (WPRM) code. Its length is
$|Y|=N=q^2+q+1$. In the present talk, we discuss how
Grobner theory is used for studying the other two
parameters: the dimension and the minimum distance
extending and generalizing the results scattered
throughout the literature. We also determine the
regularity set which helps eliminating the trivial codes
as well as giving a lower bound for the minimum
distance.<br>
<br>
This is a joint work with Yağmur Çakıroğlu (Hacettepe
University) and Jade Nardi (Université de Rennes 1).</div>
<div align="justify"><br>
</div>
<div align="left"><font color="#ff0000"><font
color="#000000"><b><font color="#ff0000">Date:<font
color="#000000"> 27 March 2026, Friday</font></font></b></font></font></div>
<div align="left"><font color="#ff0000"><font
color="#000000"><b><font color="#ff0000">Time: </font>15:40 <i>(GMT+3)</i></b><br>
<b><font color="#ff0000">Place: </font></b><font
color="#ff0000"><font color="#000000"><b>Zoom</b></font></font></font></font></div>
<blockquote>
<p><i><b>Participants who have registered will receive
the Zoom link via email one day before the
seminar.</b></i></p>
<p><i><b>If you registered for a previous talk in this
series, there's no need to register again—you'll
automatically receive the link for this session.</b></i></p>
<p><i><b moz-do-not-send="true"
href="mailto:sertoz@bilkent.edu.tr">If you haven't
registered yet, please contact <a
href="mailto:sertoz@bilkent.edu.tr"
class="moz-txt-link-freetext"
moz-do-not-send="true">sertoz@bilkent.edu.tr</a>
to be added to the mailing list.</b></i></p>
</blockquote>
<div align="left">You are most cordially invited to
attend.</div>
<div align="left"><br>
</div>
<div align="left">Ali Sinan Sertöz</div>
<div align="left"><br>
</div>
<div align="center">
<div align="center"><b><font color="#0080c0"><i><b><font
color="#0080c0"><i>This seminar series is
organized by a joint team from ODTÜ and
Bilkent<br>
<br>
Alexander Degtyarev (Bilkent)<br>
Ali Sinan Sertöz (Bilkent) contact person<br>
Ali Ulaş Özgür Kişisel (ODTÜ)<br>
Yıldıray Ozan (ODTÜ)<br>
</i></font></b></i></font></b></div>
<div align="left"><br>
</div>
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<pre cols="72">----------------------------------------------------------------------------
Ali Sinan Sertöz
Bilkent University, Department of Mathematics, 06800 Ankara, Türkiye
Office: (90)-(312) - 290 1490
Department: (90)-(312) - 266 4377
e-mail: <a href="mailto:sertoz@bilkent.edu.tr" target="_blank"
class="gmail-moz-txt-link-freetext moz-txt-link-freetext"
moz-do-not-send="true">sertoz@bilkent.edu.tr</a>
Web: <a href="http://sertoz.bilkent.edu.tr" target="_blank"
moz-do-not-send="true">sertoz.bilkent.edu.tr</a>
----------------------------------------------------------------------------</pre>
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