[Turkmath:9569] GYTE Weekly Seminars

[İrem YAMAN]

Sayın liste üyeleri,

GYTE Matematik haftalık seminerler kapsamında, Henning Stichtenoth (Sabancı Üniversitesi)
5 Mart'ta  "Rational Points on Curves over Finite Fields" başlıklı bir seminer verecektir.

Seminerin detayları ekte (ve aşağıda) olup tüm ilgilenenler davetlidir.

Saygılarımızla,
İrem Yaman & Aslı Güçlükan İlhan

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Dear All,

Henning Stichtenoth (Sabancı University) will give a talk titled "Rational Points on Curves over Finite Fields" in our next departmental weekly seminar:

Abstract:

Denote by $\mathbb{F}_q$ the finite field with $q$ elements, and by $K$ its algebraic

closure. By a {\em plane curve over} $\mathbb{F}_q$ (more precisely: an {\em irreducible affine

plane curve over} $\mathbb{F}_q$) we mean the set

$${\cal C}=\{P=(a,b)\, |\, a,b\in K \, \text{and} \, f(a,b)=0\},$$

where $f(x,y)\in \mathbb{F}_q[x,y]$ is a given irreducible polynomial with coefficients in

$\mathbb{F}_q$. We are interested in the set of $\mathbb{F}_q$-{\em rational points} of ${\cal C}$,

$${\cal C }(\mathbb{F}_q)=\{(a,b)\in {\cal C} \, |\, a,b\in \mathbb{F}_q\}$$

and in particular its cardinality

$$N({\cal C})=\#{\cal C}(\mathbb{F}_q).$$

An important numerical invariant of a curve is its {\em genus}. The famous {\em Hasse-Weil theorem}

gives upper and lower bounds for $N({\cal C})$ in terms of the genus.

In this talk I will introduce these notions and discuss some recent results

about $N({\cal C})$ for curves over $\mathbb{F}_q$ of large genus (here we will also consider

non-plane curves). Such results have interesting applications, not only in

Number Theory but also in Coding Theory, Cryptography and Theoretical

Computer Science.

Date: 05.03.2014
Time: 14:00
Location: GIT, Department of Mathematics, Building I, Seminar Room

All are most cordially invited.
Best regards,
İrem Yaman&Aslı Güçlükan İlhan



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