English

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.
The main objective of this school is to introduce modern algebraic and geometric as well as directly related methods with emphasis on those ones used in applications. Introductory courses will lay the foundations on recent developments in combinatorial algebra, tropical combinatorics, or on models in statistics like graphical models. More advanced lectures treat applied areas mentioned before (like dynamical systems), in particular their connection to algebra and geometry as well as the use of symmetries and other approaches to reduce complexity for high-dimensional phenomena. In training sessions, the participants of the school can deepen their learned skills and can discuss topics with others.
Le programme scientifique est disponible sur le site local de l'Ecole : https://sites.google.com/view/cimpa-lums2024/home?authuser=0

Langue officielle de l'Ecole : Anglais

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.
To this end, we will present theoretical and numerical courses on pharmacology, big data in health, waterborne diseases, coagulation, blood circulation, medical imaging, and. Practical sessions (using Freefem++, and python), as well as mini-projects, will also be proposed.
Le programme scientifique est disponible sur le site local de l'Ecole : https://sites.google.com/view/cimpa-silpakorn2024/

Langue officielle de l'école : anglais

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.

En effet, la théorie des structures ordonnées est par essence pluridisciplinaire. On la retrouve en logique, en algèbre, en analyse fonctionnelle, en informatique… Cette théorie se voit aussi appliquée dans plusieurs domaines telle que la Finance, l'Économie et plus récemment en Machine Learning… Ainsi nous trouverons dans cette école une série de cours sur la théorie des probabilité et de calculs stochastiques dans les treillis vectoriels et les treillis de Banach, mais aussi des cours de Machine Learning et des cours de Finance.

Le Machine Learning a connu un réel essor ces dernières décennies et est devenu un des axes les plus importants de la recherche actuelle. Il est devenu important pour la communauté scientifique des treillis vectoriels et des treillis de Banach de s’y intéresser. Ces dernières années plusieurs articles sur le Machine Learning en grande dimension ont fait appel aux treillis de Banach, laissant penser qu’une des pistes pour l’optimisation en grande dimension serait les treillis ordonné. Quelques références récentes:
- Y. Kabanov, M. Safarian, Markets with transaction costs. Mathematical theory. Springer Finance. Berlin (2009).
- Y. Korolev, Two-Layer Neural Networks with Values in a Banach Space, SIAM Journal on Mathematical Analysis Vol. 54, Iss. 6 (2022)
- H. Zhang, Y. Xu, J. Zhang, Reproducing kernel Banach spaces for machine learning. J. Mach. Learn. Res. 10, 2741-2775 (2009).

Nous avons mis l’accent sur les aspects pratiques en consacrant les après-midi de l’école à des séances de travaux dirigés ou de travaux pratiques. Les séances matinales seront plénières et se passeront dans l'amphithéâtre de l'IPEST. Les séances de l'après-midi seront en petits groupes (20 participants au maximum) et seront consacrées aux travaux dirigés et travaux pratiques. Ainsi nous avons décidé de dédoubler les séances de l'après-midi.
Le programme scientifique est disponible sur le site local de l'Ecole : https://rgosa.net/cimpa-school-osafml/

Langue officielle de l'Ecole : Anglais

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.

We will also be dealing with the security issues behind this technology, more specifically the mathematical knowledge and cryptography in modular arithmetic as well as elliptic curve cryptography. We will give a scratch lecture in the mathematics needed and then focus on the cryptographical aspects related with blockchain.

Before the school, we will give preliminary lectures (essentially
a popularization part, a cryptography part, an algorithmic and a distributed computing part). The pre-school will take place in Antsiranana at IST-D (on the same site of the school) a priori for the 20 local participants but we will set up a retransmission so that those who wish it can follow virtually these courses.
During the CIMPA school, we will form working groups among the participants that is during the school the participants will be divided into working groups
of 3, 4 or 5 people.
Le programme scientifique est disponible sur le site local de l'Ecole : https://sites.google.com/view/cimpa-antsiranana

Langue officielle de l'école : anglais

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.

Format:
-We will have four minicourses by leading experts in their fields. These minicourses will have four one hour lectures followed by 90 minutes of problem sets.
-Participants at different stages will be mixed into groups to think about the exercises.
-There will be two plenary lectures.
-In addition there will be a call for talks and posters so that students have the opportunity to present their latest work.
-We do two panels of particular topics where students can ask questions to senior professors.
Le programme scientifique est disponible sur le site local de l'Ecole : https://ecco2024.combinatoria.co/

Langue officielle de l'Ecole : Anglais

The relation between modular forms and their corresponding L-functions with various disciplines of mathematics has undergone significant evolution in the past century due to the critical role these complex analytical functions play in resolving essential problems and conjectures. The connection of modular forms and their L-functions with number theory, elliptic curves, representation theory, and algebraic geometry, among others, have resulted in diverse generalizations in different directions. The primary objective of the summer school is to acquaint graduate students in Lebanon and other regions with different types of modular forms and their practical applications.

The school is designed to be spread over two weeks, with the first week serving as an introduction to basic concepts and the second week focusing on advanced and contemporary developments. In addition to the mini-courses, the program includes a programming tutorial intended to provide students with opportunities to interact directly with the computational aspect of the theory.

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Le programme scientifique est disponible sur le site local de l'Ecole : https://www.aub.edu.lb/cams/Pages/CIMPA_2025.aspx

Langue officielle de l'Ecole : Anglais

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. The participants will be provided with an introduction to the basic material and necessary background, before proceeding to more advanced topics. The courses will survey a range of applications including classical methods of research in certain areas and applications in other modern areas, such as geometry, topology, dynamical systems, combinatorics, analysis and some other. Besides courses, we are also planning a few research talks and sessions devoted to solving exercises, open problems and discussions.
Le programme scientifique est disponible sur le site local de l'Ecole : https://sites.google.com/view/cimpa2024philippines/home

Langue officielle de l'Ecole : Anglais