[Turkmath:8201] Seminer duyurusu

[Nejla]

Merhabalar,

Prof. Dr. Arnaldo Garcia (Instituto Nacional de Matemática Pura e
Aplicada) Sabanci Universitesi'ni ziyaret etmektedir. Bu ziyaret TUBITAK
tarafindan desteklenmektedir. Bu ziyaretle de baglantılı olarak  ODTU'de iki
konusma vermektedir. Konusmaların baslıkları ve detayları aşağıda
verilmiştir. Konusmalar Ingilizce yapilmaktadir.

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Seminar  1:  On Algebraic Curves Over Finite Fields


Date: February 27, 2012, Monday, 10:30
  Place: Department of Mathematics, Room 203


Abstract

Bounding the number of points, with coordinates in a finite field, on
algebraic curves has attracted much attention, especially after the
discovery of V.D. Goppa of good linear codes from such algebraic curves.
  This talk will be a survey on Curves with Many Points, specially the
so-called maximal curves; i.e., the ones attaining Hasse-Weil upper bound
(equivalent to the validity of Riemann Hypothesis in this context).


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Seminar  2: Explicit Towers Over Non-Prime Finite Fields

Date: February 29, 2012, Wednesday, 15:30
Place: Institute of Applied Mathematics, S-209


Abstract


Bounding the number of rational points (rational places) on algebraic curves
  (function fields) over finite fields has attracted much attention.
The most famous result here is the Hasse-Weil bound which is equivalent to
the Riemann Hypothesis in this context. Ihara was the first to realize that
  the Hasse-Weil upper bound becomes weaker as the genus grows.  He then
introduced a quantity (now known as Ihara's quantity) that controls the
asymptotic on rational points (rational places) as the genus grows to
  infinity. The only situation where the exact value of this quantity is
known is the case of finite fields of square cardinalities (due to Ihara
using Shimura modular curves). Over finite fields of cubic cardinalities one
has a
  good lower bound (due to Zink and Bezerra-Garcia-Stichtenoth).
For any other cardinality (not a square or a cube) essentially nothing was
known about the behaviour of Ihara's quantity. The aim of this talk is to
  present some explicit infinite towers of curves (function fields) giving
very good lower bounds for this quantity over any non-prime finite field.
This is joint work with Bassa-Beelen-Stichtenoth.


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Prof. Dr. Arnaldo Garcia'nın Ankara ziyaretini gerçekleştirmesinde

ODTU Matematik Bolumu http://math.metu.edu.tr ODTU SIAM Ogrenci Toplulugu
http://siam.metu.edu.tr ODTU Uygulamali Matematik Enstitusu
http://www3.iam.metu.edu.tr

destek olmustur.



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