English

The central topic of the school is the mutual interaction of algebra, combinatorics and geometry. Objects of research in algebraic geometry are affine as well as projective varieties and their associated invariants which can be studied using methods from algebra and combinatorics. Toric and tropical varieties are instances where such kind of approaches were and still are very successful. In discrete geometry cones, graphs, hyperplane arrangements and matroids are examples of research subjects which naturally play prominent roles in algebra and discrete mathematics. The main goal of this school is to build bridges between various disciplines of mathematics which have in common to apply algebraic and combinatorial methods in geometry. The lectures range from the foundations to recent results and applications of the relevant theory.

Langue officielle de l'école : anglais

The school is intended for graduate students (M.Sc. and Ph.D.) and young researchers in Mathematics and Theoretical Physics of all levels. It will be dedicated to a wide range of themes on groups, Lie algebras, their representation theoretic aspects, and their applications in various fields in particular in quantization.

The first week of the school will be devoted to introductory courses on Lie groups and algebras, and mathematical quantum theory. while the second week will focus on more advanced material such as representation theory for Lie algebras, Lie algebroids and groupoids, and coherent states.

Langue officielle de l'école : anglais

The school will focus on interplay between dynamics and algebra, introducing participants to key subjects in the study of these interactions: Groupoid convolution algebras and tensor categories. The techniques developed will be applied to Leavitt path algebras, which encode combinatorics and dynamics of graphs.

Langue officielle de l'école : anglais

Geometric group theory is a relatively new line of research on its own, inspired by pioneering works of M. Dehn, G.D. Mostow and M. Gromov. It is mainly devoted to the study of countable groups by exploring connections between algebraic properties of such groups and geometric properties of spaces on which these groups act, such as the deck transformation group of a Riemannian manifold. Geometric group theory is a very broad area, and this program aims at introducing young students to different aspects of the theory.

Starting from classical results such at the Mostow rigidity theorem, we intend to build a body of knowledge to the students by introducing them to some basic material concerning hyperbolic geometry, quasi-isometry invariants and amnability, and to several modern aspects of geometric grop theory: word hyperbolic groups, boundary theory, ergodic theory and representations. 

Langue officielle de l'école : anglais

Graph Theory lies on the interface between combinatorics and discrete mathematics. The domain has expanded considerably over the last decades with interactions invarious fields such as the study of social networks, algorithms, computer science, interprobabilities, discrete geometry, producing some spectacular results.

There will be 5 mini courses of 6 hours each and 2 mini courses of 3 hours each. The courses will first introduce basic tools and the, move on to more advanced concepts in graph theory such as algorithms and their applications to computer sciences, combinatorial optimization related to linear programming, scale-free graphs, spectral theory, the theory of infinite graphs. Applications will include models of the internet, social networks, small world phenomena, also discrete geometry and probability theory. 

Langue officielle de l'école : anglais

A complex number is called algebraic if it is a root of a non-constant polynomial with integer coefficients and is transcendental otherwise. Over recent decades, the transcendental nature of special values of certain arithmetic functions which verify functional equations has been a fascinating branch of Number Theory and attracts an incredible number of work. However, beautiful mysteries remain unsolved.

This CIMPA school aims to familiarize graduate students and young researchers to basic concepts and tools of Differential Galois Theory, Diophantine Geometry, Transcendental Number Theory and introduce them to some beautiful theorems about the transcendence of values of particular functions such as the modular j-function, zeta functions, M-functions.

Three introductory courses and three advanced courses will be given by leading experts in their fields. It will be suitable for motivating participants to gain entry into the theory and to discover some of the cutting-edge research problems in Modern Number Theory.

Langue officielle de l'école : anglais

The school will focus on some stochastic aspects of mathematics and on algorithms used in this context. More precisely, classical random structures such as Markov chains, random walks, discrete combinatorial structures, random texts, chaotic dynamical systems will be considered and some tools to study them, mainly analytic combinatorics, will be given.

A course will be given on finite Markov chains for optimization with applications to famous problems such as Traveling Salesman Problem and Scheduling. Another course will be on random walks with related topics such as Brownian motion, Lattice walks and structural properties of the associated generating functions. A course will also be provided on bioinformatics and linguistics with use of methods such as formal languages, automata and use of generating functions. Moreover, a course will be dedicated to the analytic tools used for the previous course which includes Cauchy integral, combinatorics of structures, generalized central limit law, Mellin integral.

Chaotic dynamical systems will be considered as random source. A tutorial for the free computer algebra system SageMath and a course on statistics language R will be scheduled.

Langue officielle de l'école : anglais

Although cryptography has a long history, it has developed during the 20th century into a modern science with the help of computer science and mathematical objects coming from algebra, number theory, geometry, combinatorics,...

The school will present modern aspects of cryptography based on number theory, algebra, and algebraic geometry. The courses will present various aspects of the subject: elementary and algebraic number theory, elliptic curves, lattices, computational aspects, and their use in cryptography. Training sessions will be devoted to PARI/GP or SageMath, two efficient computer algebra systems which are open-source and widely used by the community.

The school aims at promoting and developing these new research areas for teachers and researchers in Senegal, attracting new students and developing scientific collaborations with other countries, including co-directions of Ph.D. students.

Langues officielles de l'école : anglais et français

This  school  aims  to  introduce  young  researchers  and  students  to  actual research  problems  in  the  field  of  tilings,  packings  and  optimization.  In particular,  we  shall  focus  on  possible  original  interactions between  these thematics, as well  as connections with more classic fields as number theory, transportation modeling or word combinatorics. There shall be six long courses, which consist of lectures as well as training sessions (at least half of the time – since  it  is  the  best  way  to  see  what  participants  with  very  different backgrounds really understand). We also plane an « open problem » session, the goal of which is to propose possible new research axes to the participants. An excursion is  planned the  first  day  in  order  to  facilitate  contact  among participants and lecturers for the rest of the week (the goal of sport activities is similar).

Langue officielle de l'école: anglais

The aim of this school is to promote the development of mathematics in Madagascar, especially in the area of non-associative algebra, providing new research opportunities for the professors and post-graduate students from the University of Antananarivo and other Malagasy universities.

Topics of school include Non-associative algebras, Deformations, Lie algebras, Leibniz algebras and Computational Methods.

Langue officielle de l'Ecole: anglais