[Turkmath:7439] ODTU-Bilkent Algebraic Geometry Seminar-Zoom-582

[Ali Sinan Sertöz]

*Welcome to the 2026 Spring talks of ODTÜ-Bilkent Algebraic Geometry 
Seminars**
*
/since 2000/
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This week the ODTÜ-Bilkent Algebraic Geometry Seminar 
<http://www.bilkent.edu.tr/~sertoz/agseminar.htm>  is *online*

/This talk will begin at _*15:40*__ (GMT+3)_/
Please check your time difference between Ankara and your city here 
<https://www.timeanddate.com/worldclock/fixedtime.html?msg=ODT%C3%9C-Bilkent+Algebraic+Geometry+Seminar&iso=20260327T1540&p1=19&ah=1>
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*

/Ben Viegers (1886-1947)
/
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**Speaker: Mesut Şahin <https://avesis.hacettepe.edu.tr/mesut.sahin>**
******Affiliation: /Hacettepe

/**
**Title:  Grobner Bases and Linear Codes on Weighted Projective Planes
**
**Abstract:**  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 $K$.

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.

This is a joint work with Yağmur Çakıroğlu (Hacettepe University) and 
Jade Nardi (Université de Rennes 1).

*Date: 27 March 2026, Friday*
*Time: 15:40 /(GMT+3)/*
*Place: **Zoom*

    /*Participants who have registered will receive the Zoom link via
    email one day before the seminar.*/

    /*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.*/

    /*If you haven't registered yet, please contact
    sertoz at bilkent.edu.tr to be added to the mailing list.*/

You are most cordially invited to attend.

Ali Sinan Sertöz

*/*/This seminar series is organized by a joint team from ODTÜ and Bilkent

Alexander Degtyarev (Bilkent)
Ali Sinan Sertöz (Bilkent) contact person
Ali Ulaş Özgür Kişisel (ODTÜ)
Yıldıray Ozan (ODTÜ)
/*/*


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Ali Sinan Sertöz
Bilkent University, Department of Mathematics, 06800 Ankara, Türkiye
Office: (90)-(312) - 290 1490
Department: (90)-(312) - 266 4377
e-mail:sertoz at bilkent.edu.tr <mailto:sertoz at bilkent.edu.tr> 
Web:sertoz.bilkent.edu.tr <http://sertoz.bilkent.edu.tr> 
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