[Turkmath:8172] Workshop on Towers of Function Fields, February 23-24, 2012

[Alp Bassa]

Değerli Liste Üyeleri,

23-24 Şubat 2012 tarihleri arasında SU Minerva Palas'da düzenlenecek olan
"Towers of Function Fields" calıştayı ile ilgili aşağıdaki duyuruyu
dikkatinize sunarım.

Saygılarımla,
Alp Bassa


Dear List Members,

on February 23-24, 2012, we are organizing a workshop on "Towers of
Function Fields" at SU Minerva Palace, Karaköy.

For the program, titles/abstracts of the talks, please see below or
*http://sccc.sabanciuniv.edu/en/towersworkshop*

For information on how to reach SU, Minerva Palace, please see
http://www.sabanciuniv.edu/eng/?kampus_hayati/hizmet_ve_olanaklar/adres_ve_ulasim_krokisi.html

For more information on the ongoing "Semester on Curves, Codes,
Cryptography", please see
http://sccc.sabanciuniv.edu/

This workshop is supported by Sabanci University. The visit of A. Garcia to
Sabanci University is supported by Tübitak.

All the Best

Alp Bassa

***************************
Workshop "Towers of Function Fields", February 23-24 2012, Sabanci
University,  Minerva Palace, Bankalar Caddesi 2, Karaköy, İstanbul

*Program*
*February 23, Thursday*
09.30 - 10.30  Michael Tsfasman (Institute for Information Transmission
Problems and Independent University of Moscow)
        Sphere packings in large dimensions
10.45 - 11.45  Henning Stichtenoth (Sabanci University, Istanbul)
        Explicit towers over non-prime finite fields I
14.00 - 15.00  Arnaldo Garcia (IMPA, Rio de Janeiro)
        Explicit towers over non-prime finite fields II
15.30 - 16.30  Stephane Ballet (Institut de Mathematiques de Luminy,
Marseille)
        Class numbers in algebraic function fields defined over finite
fields, and related problems
16.45 - 17.45  Ignacio Cascudo (CWI, Amsterdam)
        Arithmetic codices
19.00 Workshop dinner (details will be announced at the workshop)

*February 24, Friday*
09.30 - 10.30  Marc Perret (Institut de mathematique de Toulouse)
        Some remarks on the  loci of decomposed and of singular points in
recursive towers
10.45 - 11.45  Kit-Ho Mak (University of Illinois at Urbana-Champaign)
        On lower bounds for the Ihara constants A(2) and A(3)
14.00 - 15.00  Peter Beelen (DTU, Copenhagen)
        Explicit towers over non-prime finite fields III
15.30 - 16.30  Alp Bassa (Sabanci University, Istanbul)
        Explicit towers over non-prime finite fields IV


*Abstracts:*
*
*
Ballet: Class numbers in algebraic function fields defined over finite
fields, and related problems
We give lower bounds for the class number in algebraic function fields
defined over finite fields, which improve the Lachaud - Martin-Deschamps
bounds. We give examples of towers of algebraic function fields having a
large class number and we present related problems.

Bassa, Beelen, Garcia, Stichtenoth: Explicit towers over non-prime finite
fields I-IV
A new family of towers over any non-prime finite field is presented. These
towers are recursively defined, and they have a surprisingly large limit.
For quadratic base fields, the Drinfeld-Vladut bound is attained; for cubic
base fields, the Zink bound is attained. For all other finite base fields,
the limit of the tower is much larger than the limits of previously known
families of function fields. Hence we obtain a significant improvement of
lower bounds for Ihara's quantity A(q), for all q=p^n with odd n > 3.

Cascudo: Arithmetic codices
In this talk I will present the notion of arithmetic codices, recently
introduced in joint work with Ronald Cramer (CWI Amsterdam) and Chaoping
Xing (NTU Singapore). Arithmetic codices have important applications in
cryptography (in secure multiparty and two party computation) and in the
complexity of multiplications in extension fields. Good towers of function
fields provide the only known way of constructing 'asymptotically good
families' of codices. In addition, I will motivate our introduction and
study of what we have called the 'torsion limit' of a tower.

Mak: On lower bounds for the Ihara constants A(2) and A(3)
Let F_q be the finite field with q elements. The Ihara constant A(q) is an
asymptotic measure of how many points a curve over F_q can have compared to
its genus when the genus goes to infinity. In this talk, we will describe
how to improve the best known lower bounds for A(2) and A(3). This is joint
work with I. Duursma.

Perret: Some remarks on the loci of decomposed and of singular points in
recursive towers
With the help of a graph closely related to Beelen's one and to
intersection theory on surfaces, we will give some insights into the sets
of decomposed points and of singular points in good recursive towers.
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