English

This summer school focuses on number theory and its practical applications in cryptography and coding theory. Broadly speaking, number theory investigates properties of integers, including primes and solutions of Diophantine equations. Despite being a very ancient branch of mathematics, number theory very much remains a dynamic branch of mathematics, with ongoing research uncovering impressive results every year, and with new puzzling questions regularly surfacing. In recent decades, number theory has come to play a pivotal role in numerous real-life problems : for instance, prime numbers and their properties lie at the heart of the algorithms used to secure online payments. With the rapid development of computing technologies, it is actually fair to say that number theory takes a rapidly growing importance in cryptography and coding theory.

Our summer school aims to bridge theory and practice by providing students both with introductions to several key areas of number theory, and with a hands-on understanding of some of their prominent applications in cryptography and coding theory. Our summer school offers four courses in fundamental number theory, focusing on important topics such as number fields, elliptic curves, lattices, and modular forms. While these courses delve into theoretical aspects, we've designed them to include concrete examples and hands-on exercises to help students grasp the practical applications of these concepts. Additionally, we provide a series of courses exploring how these mathematical notions are being applied in cryptography and coding theory. These courses emphasize real-world examples, self-programmed protocol implementations, and hands-on applications.

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Le programme scientifique est disponible sur le site local de l'école :
http://www.rnta.eu/Yogyakarta2025/index.html

Langue officielle de l'école : anglais

The school aims to introduce graduate students and young researchers to modern algebra and its applications, with a focus on Tits-Kantor-Koecher construction, Jordan algebras, Rota-Baxter Lie algebras and some non-associative algebras, such as Lie algebras, Jordan algebras, automorphisms, derivations and cohomology of classical and quantum algebras and their applications in other areas of mathematics. The courses will deal with a description of certain algebraic systems, their classifi cation, and their 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.

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Le programme scientifique est disponible sur le site local de l'école :
https://sites.google.com/view/cimpa2025uzbekistan/program

Langue officielle de l'école : anglais

The goal of the summer school is to introduce students and junior scientists to the basics of the theory of elliptic curves and their applications in modern number theory and cryptography. The origins of the theory of elliptic curves go back to the 19th century, but it has become a central area of number theory only in the 20th century with the work of Mordell, Hasse, Weil and many others. Particularly prominent developments were the formulation of the conjecture of Birch and Swinnerton-Dyer, and the discovery of connections between elliptic curves and modular forms. Elliptic curves also have come to play an important role in modern cryptography, and they continue to be extensively studied for possible future crypto systems resistant to quantum computing. Hands-on approach based on exploring examples rather than giving formal proofs will be followed by all instructors.

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Le programme scientifique est disponible sur le site local de l'école :
https://sites.google.com/view/ecasummerschool2025

Langue officielle de l'école : anglais

The aim of this CIMPA school will be to familiarise graduate students and young researchers with the field of enumerative and analytic combinatorics, and to show its many connections to other areas, especially computer science.

The courses range from introductory to more advanced levels. The introductory courses will lay the groundwork by discussing the basic concepts (such as generating functions and enumeration methods) and techniques (various enumeration techniques and analytic methods such as singularity analysis). Then, techniques relating to particular combinatorial objects will be discussed, covering partitions, trees, and permutations as objects. Practical courses in SageMath covering packages and techniques used in this type of combinatorics will be given.

In the final week of the school, some afternoons will be spent forming small research groups. It is hoped that these research groups will continue online after the school.

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Le programme scientifique est disponible sur le site local de l'école :
https://math.sun.ac.za/cimpa/

Langue officielle de l'école : anglais

The school aims to bring participants acquainted with the latest advances in K-theory and Operator Algebras. I will consist of 2 parts; a preliminary set of 4 virtual courses, and second part, the school proper, consisting of 8 presential courses on more advanced topics.
The preliminary virtual courses are intended to provide participants the necessary background. They will take place syncronically 2 weeks before the school begins, so participants will have a week to digest the material. Each of these courses will be three lectures long; the lectures will be recorded. The recordings, slides and any other course material will be made available to participants.
The actual school will consist of eight courses spread along 2 weeks, with the first week taking place in La Plata and the second in Buenos Aires. Each of the courses of the first week is thematically connected with one of the second, with the first course being introductory and the second more advanced. The structure of each course will consist of 3 lectures and one problem session. In addition there will be a "gong show" each week in which participants will be given the opportunity to very briefly explain their work. In addition there will be a round table concerning gender in the mathematical profession.

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Le programme scientifique est disponible sur le site local de l'école :
https://65f2082f6e9e0.site123.me

Langue officielle de l'école : anglais

Mathematical and statistical modeling in oncology is a multidisciplinary field that applies mathematical and statistical techniques to understand, describe, and predict various aspects of cancer biology, epidemiology, and treatment. It plays a crucial role in advancing our understanding of cancer, optimizing treatment strategies, and informing healthcare decision-making. Some key areas of research within this field include: developing mathematical models to describe how tumors grow, evolve, and spread within the body, quantifying the behavior of cancer drugs in the body and optimizing treatment strategies; studying the incidence and prevalence of cancer, identifying risk factors, and predicting cancer trends; tailoring cancer treatment plans to individual patients based on genetic and clinical data; designing statistically rigorous clinical trials to evaluate the effectiveness of new cancer treatments.
The school is designed to provide participants with in-depth knowledge and skills in the application of mathematical and statistical techniques to cancer research. The goal is to equip participants with the tools and expertise necessary to address complex problems in oncology using quantitative methods. It aims to contribute to bridge the gap between mathematics, statistics, and medicine to advance our understanding of cancer and improve patient outcomes.
Participants of the school can expect to gain a deep understanding of both the theoretical foundations and practical applications of mathematical and statistical techniques in the context of cancer research. Here are some specific learning outcomes. Participants will learn how to formulate mathematical models to describe cancer-related processes, such as tumor growth, metastasis, and treatment response. They will acquire expertise in statistical methods for analyzing clinical and experimental data, including survival analysis, regression analysis, and hypothesis testing. They will learn how to integrate data from various sources, such as genomics, imaging, and clinical records, to gain insights into cancer biology and patient outcomes. Proficiency in programming languages commonly used in mathematical and statistical modeling, such as R, Python, will be taught to implement and simulate models.
Understanding the clinical and biological context of cancer research is crucial, so participants will gain knowledge of cancer biology and relevant medical terminology.
Collaboration skills will be emphasized, as participants will likely work with researchers from diverse backgrounds, including oncologists, biologists, and statisticians.

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Le programme scientifique est disponible sur le site local de l'école :
https://natural-sciences.nwu.ac.za/paa/3MC-CIMPA-School-2025

Langue officielle de l'école : anglais

The goals of the research school we propose are: first, to gather young researchers in order to provide them the basics on Leavitt path algebras, Hochschild (co)homology, K-theory and related topics and also a glimpse of the state of art in the ongoing research carried out within the fields which comprise the subject of Leavitt path algebras, Hochschild (co)homology and K-theory; second, to provide the audience a general view of the results which have been achieved; and, finally, to give a broad picture of some of the research lines which are currently being pursued. There would be some introductory courses on Representation Theory, Hochschild (co)homology, K-Theory, and Leavitt path algebras. Besides courses, we are also planning a few research talks and sessions devoted to solving exercises, open problems and discussions.

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Le programme scientifique est disponible sur le site local de l'école :
https://cimpa2025hefei.ahu.edu.cn

Langue officielle de l'école : anglais

The research school's program is oriented in such a way as to make listeners benefit from the latest advances in the field of Machine Learning, Deep Learning and other data science techniques. The artificial intelligence and statistics community, and that of scientific computing have come together in recent years to give birth to new algorithms useful to both themes. Indeed, the first community by being interested in large-scale problems, appropriated a certain number of methods usually used by the second. Similarly, the scientific computing community for solving problems arising from physics has begun to take a close interest in Machine Learning and Deep Learning techniques to develop economic models in computing time. It is to these highly intriguing questions that the lecturers of this school will focus.

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Le programme scientifique est disponible sur le site local de l'école :
http://cimpa2025.lamsin.tn   

Langue officielle de l'école : anglais

An $L$-function is a function defined additively by a Dirichlet series with a multiplicative Euler product.
The initial work of Dirichlet was generalized to number fields by Hecke and given an adelic interpretation by Tate
which paved the way to move from $GL(1)$ to higher degree $L$ functions associated to automorphic forms of $GL(n)$ for a general n .

Automorphic $L$ functions are essentially analytic objects and allow translations between arithmetic and analysis.
We recall the legendary correspondence in the case of the
Riemann-$zeta$ function, the prototype of higher $L$-functions both analytic and arithmetic-algebraic,
between an arithmetic statement on the distribution of primes and an analytic one on the distribution of its zeros.
Now there are many more parameters to explore.
For example, bounding twisted automorphic forms in terms of conductors help obtain the asymptotics of representations
of totally positive integers by ternary quadratic forms.

The aim of this school is to prepare the participants to appreciate the contemporary theory of automorphic representations, their $L$-functions
and their surprising links with diverse fields like Fourier analysis, algebraic geometry and theoretical physics.

Le programme scientifique est disponible sur le site local de l'école :
https://www.mathconf.org/alfiitr2024

Langue officielle de l'école : anglais

The purpose of the school is to present a self-contained proof of a famous theorem of Serre in 1972. This theorem tells us that the representation associated to the Galois action on the p-torsion points of an elliptic curve is surjective for p great enough. This theorem had a very great impact in the field of arithmetic geometry and opened the field to numerous problems that are, for some, still open today. After introducing the students to the topics needed to understand the proof, illustrating the theory through exercises and sessions on computer, we will present the proof itself.

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Le programme scientifique est disponible sur le site local de l'école :
http://www.rnta.eu/Valparaiso25

Langue officielle de l'école : anglais