METU SIAM Student Chapter

Speaker: Dr. Arnaldo Garcia

Researcher at Instituto Nacional de Matematica Pura e Aplicada, IMPA
www.impa.br/opencms/pt

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).

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.

Institute of Applied Mathematics, http://www3.iam.metu.edu.tr
Society for Industrial and Applied Mathematics, http://siam.org
Department of Mathematics, http://math.metu.edu.tr

Speaker’s visit to Turkey is supported by Tubitak.

The application stage of  our first ever research competition is now over. We thank all of our fellow students for their applications! Those who complete the first stage of evaluation successfully will be announced on this page in the coming weeks.

A METU student is to present her/his research at the SIAM Annual Meeting, July 10,2012 in Minneapolis, Minnesota, USA. Every year only six student chapters from all over the world are invited and this year our chapter has been selected as one of these six.

Our chapter is inviting fellow students to submit their research for consideration to be the representative of our chapter at this meeting.

SIAM = Society for Industrial and Applied Mathematics. All research in engineering, sciences, economics, management  and other fields that uses applied math is welcome.

A support of at least $1000 will be available for the student that will be selected.

If you satisfy the eligibility requirements indicated below please submit your manuscript to metusiam@gmail.com by February 8th, 2012, Wednesday, Midnight.

Support

SIAM will provide $750 to cover travel and accommodation expenses. Additional $250 will be available from our chapter.  We hope to get additional support from our university.

Description

The METU SIAM student chapter is inviting you to apply to

1. Present your research during Student Days on July 10, 2012, as part of the 2012 SIAM Annual Meeting in Minneapolis, Minnesota, USA. Every year only six student chapters from all over the world are invited;
2. Represent our chapter at the Chapter Meeting with SIAM Leadership.
3. Have the title of your research included in the April issue of SIAM News in a special insert about the SIAM Annual Meeting.

Eligibility

Any PhD, Masters, or senior undergraduate student may apply. The student has to be a member of the SIAM Student Chapter (any METU student can become a member by contacting the Chapter at metusiam@gmail.com). If the work to be presented is based on the Masters or PhD thesis of the student, the defense date of the thesis must be after January 1, 2011. If the work to be presented is based on a paper, the first submission date of the paper to any journal must be after January 1, 2011

Deadline

If you satisfy the eligibility requirements please submit your manuscript to metusiam@gmail.com by February 8th, 2012, Wednesday, Midnight.

Websites related to the event

METU SIAM Student Chapter: http://siam.metu.edu.tr
SIAM Global website: http://siam.org
SIAM Annual meeting website: http://www.siam.org/meetings/an12/index.php
SIAM News: http://www.siam.org/news/
METU SIAM Student Chapter is sponsored by the Institute of Applied Mathematics and the Department of Mathematics. Institute website: http://www3.iam.metu.edu.tr,  Math dept. website: http://math.metu.edu.tr

Our poster for this event is below: