2025

Lecturer: Christophe RITZENTHALER

Abstract

This mini-course is a motivated introduction to the problematic of number of rational points on curves over finite fields. It will serve as a pretext to introduce the basics of algebraic geometry (Nullstellensatz, projective geometry,...) with a far-away open problem in mind (distribution of the number of points on genus 4 curves). We will in particular try to reduce the number of coefficients of these curves to be able to run some experiments with a computer.

Jorge Mozo Fernández

Summary: The idea of this course is to give an introduction to the theory of real dynamical systems from scratch, focusing on the main elements of qualitative theory: equilibria, periodic orbits, limit cycles, … An outline of the contents is as follows:

Coordinators: Hacen Zelaci (zelaci-hacen@univ-eloued.dz) & Adrien Boulanger, Aix-Marseille Université, France (adrien.boulanger@univ-amu.fr)

Coordinators: Celestin Kurujyibwami,(celeku@yahoo.fr) & Balazs Szendroi, University of Vienna,

Austria (balazs.szendroi@univie.ac.at) & Emanuel Carneiro, ICTP, Italy (carneiro@ictp.it)

Coordinators: Régis Freguin BABINDAMANA (regis.babindamana@umng.cg) & Christian Maire, Université de Franche-Comté, France (christian.maire@univ-fcomte.fr)

Coordinators: Armel Fabrice Evrard YODE (yode.fabrice@ufhb.edu.ci) & Anne-Françoise YAO, Université Clermont Auvergne et École Polytechnique Paris, France (anne.yao@uca.fr).

Coordinators: Koffi Wilfrid HOUEDANOU (khouedanou@yahoo.fr) & Guy Aymard DEGLA, ICTP, Italy (gdegla@imsp-uac.org)

Coordinators: Çağatay Yıldız, University of Tübingen, Germany (cagatay.yildiz@uni-tuebingen.de) & Özgür Martin, Mimar Sinan Fine Arts University, Turkey (ozgur.martin@msgsu.edu.tr).

Coordinator: Ezgi Kantarcı Oğuz (ezgikantarcioguz@gmail.com)

Coordinator: Feride Ceren Köse, University of Georgia (fceren@uga.edu)