2024

The school aims at introducing the students to a few lines of research in number theory revolving around the concepts of lattices, heights and diophantine approximation. Part of the school is devoted to presenting the recent proof by Maryna Viazovska that the densest sphere packing in dimension 8 is the one given by the E_8 lattice. In 2022 she was awarded the Fields medal. To this end we introduce the students to lattices, sphere packings and modular forms.

The school aims to introduce graduate students and young researchers to modern algebra and its applications, with a focus on Leavitt path algebras, Shift algebras and some non-associative algebras, such as Lie algebras, Jordan algebras, Poisson algebras and their applications in other areas of mathematics, e.g. geometry, topology and analysis, and in theoretical physics. The courses will deal with a description of certain algebraic systems, their classification and connection with other algebraic systems.

Cutting-edge challenges in science require up-to-date methods, especially if high-dimensional data is involved in areas like data analysis or machine learning. The overriding topic of this CIMPA school is recent developments in algebra and geometry with a strong focus on applications. Chemical reaction networks, dynamical systems, and optimization are examples of fields where sophisticated tools from algebraic statistics, combinatorics, toric geometry, or tropical geometry have been applied successfully in the past years.

Ce projet d’Ecole CIMPA est destiné à introduire des cours sur les Equations aux Dérivées Partielles (EDP), exposer les méthodes numériques pour la résolution des EDP ainsi que la modélisation et la simulation de certains phénomènes à l’aide des EDP.

The aim of the school is to introduce participants to several numerical techniques and analysis in Partial Differential Equations (PDEs). The topics to be treated will vary from standard contemporary schemes to recent advances in the numerical treatment of PDEs and numerical linear algebra techniques. Some of the other topics to be presented during the school are: model order reductions, pde constrained optimal control and inverse problems.

The area of the school will be mathematical analysis, modeling, data analysis, scientific computing to address real problems in medicine and health sciences. Our goal is to prepare students and researchers for the concrete problems arising from mathematical modeling in medicine, which may arise particularly in South-East Asia.

Le contenu se veut pluridisciplinaire tout en favorisant les interactions entre les différentes spécialités proposées.

Ainsi cette école se reposera sur deux axes : la finance mathématique et le calcul stochastique d’un côté et le machine learning de l’autre. Ces deux axes seront par ailleurs traités via le point vue « Ordre », i.e. les structures ordonnées.

The aim of this school is to introduce students to some aspect of (algorithmic) number theory and arithmetic geometry and the very fruitful interplay between those subjects and the applied disciplines of cryptography and coding theory. Our program consists of four courses on algorithmic number theory, elliptic curves, algebraic coding theory and isogeny based cryptography, respectively. These courses will introduce the students to a variety of tools in number theory and arithmetic geometry as well as their applications in cryptography and coding theory.

In this school we will focus on two branches of blockchain technology. First, the development of blockchain technology including subjects such as the tokening ofactivities, fintech, proptech, insurtech, e-health, eGovernment, supply chain and social services, among other things.

Combinatorics is at the centre of a variety of areas in pure and applied mathematics. For
instance, in recent years problems arising in algebra and geometry have been better understood
and in many cases fully solved by exploiting their relation to certain discrete objects.
At this school we aim to explore modern geometric techniques that have been used in recent
years to solve long standing conjectures in combinatorics and other areas.