[Turkmath:6132] Hacettepe Üniversitesi Genel Semineri-Jade Nardi

[Asli Pekcan]

Sayın Liste Üyeleri,

Hacettepe Üniversitesi Matematik Bölümü genel seminerleri kapsamında, 31 Mayıs
2023 tarihinde saat 15:00'te, Zoom üzerinden Rennes Üniversitesi'nden Jade
Nardi'nin vereceği ''*Error correction from toric varieties: toric codes
and their locality**'*' başlıklı konuşmaya ilgilenen herkesi
bekleriz. Konuşma özeti ve zoom bağlantı bilgileri aşağıda yer almaktadır.

Saygılarımla,

Prof. Dr. Aslı Pekcan Yıldız
Seminer Koordinatörü
---------------------------------------------------------------------------------------------------------------
https://us06web.zoom.us/j/87472510662?pwd=aHc3ajdYVnJFL2dKWkVWU2trUFBnQT09
<https://www.google.com/url?q=https://us06web.zoom.us/j/87472510662?pwd%3DaHc3ajdYVnJFL2dKWkVWU2trUFBnQT09&sa=D&source=calendar&usd=2&usg=AOvVaw3ilk0OuxoVKW28IZoyf39u>
Toplantı Kimliği: 874 7251 0662
Parola: 258177
------------------------------
----------------------------------------------------------------------------------------
*Konuşmacı*: Jade Nardi
*Konuşma Başlığı*: Error correction from toric varieties: toric codes and
their locality
*Konuşma Özeti: *All the signals sent through noisy communication channels
(telephone, radio waves, Internet optical fibre...) are likely to be
degraded during the transmission. To make sure that the messages sent are
correctly received, we use a tool that is omnipresent in today's
telecommunications, which is at the frontier between mathematics and
computer science: error-correcting codes. In this talk, we will focus on
linear error-correcting codes. Mathematically speaking, these are just
vector spaces over a finite field. Their structure ensures that, even if
errors occur during transmission, the receiver of the message can detect
and even correct them.
In this talk, we will be interested in toric codes, which are a family of
linear error-correcting codes that comes from algebraic geometry and
combinatorics. They consist of vector spaces spanned by the evaluation of
some monomials at the elements of a finite field. When evaluating
univariate polynomials of bounded degree, we get the well-known
Reed-Solomon codes, which have optimal correction capability and efficient
decoding algorithms. By allowing multivariate polynomials, efficiency
parameters may deteriorate, and the decoding is much less obvious. However,
for a given base field, we get longer codes and, above all, we gain
locality, i.e. the possibility to correct a symbol by accessing a few other
symbols of a codeword. After giving a short presentation about linear
error-correcting codes and introducing toric codes, we will present how
toric codes are naturally endowed with locality and how this property can
be used for applications to information theory.
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://yunus.listweb.bilkent.edu.tr/pipermail/turkmath/attachments/20230525/55f52dc8/attachment.html>