Centre International de Mathématiques Pures et Appliquées

CIMPA-ICTP-UNESCO-MESR-MINECO-PHILIPPINES research school

A joint CIMPA-ICTP research school

Objectives :

The theory of algebraic curves over finite fields is a very active subject both from a theoretical and an applied point of view. The research school aims to cover theoretical, computational and applied aspects of the topic and thus will be useful to a broad range of students and young mathematicians interested in algebra and its applications.

The research school will develop the subject almost from scratch, beginning from introductory classes on finite fields and algebraic curves. We will cover aspects of the theory of elliptic curves over finite fields as well as the application of the Riemann-Roch theorem to the zeta function of an algebraic curve over a finite field (including the Stepanov- Bombieri-Schmidt proof of the Riemann hypothesis). Applications will also figure prominently with sessions on elliptic curve cryptography, coding theory and computational examples using Pari GP and Sage. Moreover we plan to cover the explicit construction of elliptic curves over finite fields with group of points of large prime order (as needed by cryptographic applications) via complex multiplication. The local organizers are considering conducting a one-week preparatory program for participants who may not be prepared to handle the advanced topics in the research school. Lectures in the preparatory program will be given by local mathematicians.

Administrative and scientific coordinators

 Fidel Nemenzo (University of the Philippines Diliman), fidel@math.upd.edu.ph
 Michel Waldschmidt (Université Pierre et Marie Curie - Paris 6), miw@math.jussieu.fr

Scientific Committee :

 Fidel Nemenzo (University of the Philippines Diliman)
 Francesco Pappalardi (Università "Roma Tre")
 Valerio Talamanca (Università "Roma Tre")
 Jorge Jimenez Urroz (Universitat Politècnica de Catalunya)
 Michel Waldschmidt (Université Pierre et Marie Curie - Paris 6)

Local Organizing Committee :

 Fidel Nemenzo (University of the Philippines Diliman)
 Julius Basilla (University of the Philippines Diliman)
 Richell Celeste (University of the Philippines Diliman)

Date and location :

July 22-August 2, 2013, University of the Phillipines Dillman, Manila, Philippines

Scientific Program :

All courses will be given in English

First week

1. Finite fields : Michel Waldschmidt (Paris 6)
2. Introduction to Coding Theory : Pierre Arnoux(Luminy)
3. Explicit construction of elliptic curves : Peter Stevenhagen (Leiden)
4. Elliptic Curves over Finite Fields : Francesco Pappalardi(Roma Tre)

Second week

1. Algebraic curves and the Riemann-Roch Theorem (Roma Tre) : Valerio Talamanca
2. Distribution of irredicubile polynomials over finite fields : Paul Pollack(UCB)
3. Zeta series and applications : René Schoof(Tor Vergata)
4. Elliptic Curves Criptography : Jorge Jiménez Urroz(UPC Barcelona)
5. Elliptic curves modulo primes : Alina Cojocaru(University of Illinois at Chicago)

The course Computation using PARI and SAGE by Corrado Falcolini (Roma Tre) will be spread over the two weeks.

Deadline for registration :

April 21, 2013

Application procedure and Online registration only for applicants not from Philippines.

Applicants from Philippines must contact the local organizer : Fidel Nemenzo (fidel at math.upd.edu.ph)

School website