[Turkmath:6086] ODTU-Bilkent Algebraic Geometry Seminar-Zoom-528

[Ali Sinan Sertöz]

*Welcome to the 2023 Spring talks of ODTU-Bilkent Algebraic Geometry 
Seminars**
*
/since 2000/
**=================================================================**

This week the ODTU-Bilkent Algebraic Geometry Seminar 
<http://www.bilkent.edu.tr/~sertoz/agseminar.htm>  is *online*

/This talk will begin at _*15:00*__ (GMT+3) <<--New time
_/
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=20230428T15&p1=19>
*=================================================================*
**
/Edouard Leon Cortes (1882-1969)
/

**Speaker:Mesut Şahin <https://avesis.hacettepe.edu.tr/mesut.sahin>
****Affiliation: /Hacettepe/****
Title:Vanishing Ideals and Codes on Toric Varieties

**
**Abstract:**
Motivated by applications to the theory of error-correcting codes, we 
give an algorithmic method for computing a generating set for the ideal 
generated by $\beta$-graded polynomials vanishing on a subset of a 
simplicial complete toric variety $X$ over a finite field 
$\mathbb{F}_q$, parameterized by rational functions, where $\beta$ is a 
$d\times r$ matrix whose columns generate a subsemigroup 
$\mathbb{N}\beta$ of $\mathbb{N}^d$. We also give a method for computing 
the vanishing ideal of the set of $\mathbb{F}_q$-rational points of $X$. 
We talk about some of its algebraic invariants related to basic 
parameters of the corresponding evaluation code. When $\beta=[w_1 \cdots 
w_r]$ is a row matrix corresponding to a numerical semigroup 
$\mathbb{N}\beta=\langle w_1,\dots,w_r \rangle$, $X$ is a weighted 
projective space and generators of its vanishing ideal is related to the 
generators of the defining (toric) ideals of some numerical semigroup 
rings corresponding to semigroups generated by subsets of 
$\{w_1,\dots,w_r\}$.

*Date:28 April 2023*, *Friday*
*Time: 10:40 /(GMT+3) <<<<<<<<<Notice the new start time <<<<<<<<<< /*
*Place: **Zoom*

    **One day before the seminar, an announcement with the Zoom meeting
    link will be sent to those who registered with Sertöz.
    **

    **If you have registered before for one of the previous talks, there
    is no need to register again; you will automatically receive a link
    for this talk too.
    **

    **If you have not registered before, please contact him at
    sertoz at bilkent.edu.tr
    <mailto:sertoz at bilkent.edu.tr?subject=Zoom%20Seminar%20Address%20Request>.**


You are most cordially invited to attend.

Ali Sinan Sertöz
/(PS: To unsubscribe from this list please send me a note.)/
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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
Fax: (90)-(312) - 290 1797
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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