English

The school aims at introducing graduate students and young researchers to the mathematic of climate science. Lectures will cover key topics in the field focusing on their mathematical complexity and dimension. Climate science is genuinely interdisciplinary and this is reflected in the breath of topics offered in the school: predictability, data assimilation, climate prediction, climate sensitivity and thermodynamics. The mathematics to address and understand these problems will be the characteristic of the school and will include dynamical system, statistics, numer­ical methods, statistical mechanics and linear algebra. The lectures will start by presenting the phys­ical concrete challenge and then will focus on the mathematical tools and concept used to solve them. At the same time, there will be tutorials with practical problems to be solved by the students under
the mentors' guidance.

Langue officielle de l'Ecole: anglais

The main theme of the proposed school are graph algebras, which are objects of growing interest that lie at the boundary between algebra and analysis among other mathematical fields. Despite being introduced only about a decade ago, Leavitt path algebras, as algebraic counterpart of graph C ∗ -algebras, have arisen in a variety of different contexts as diverse as symbolic dynamics, noncommutative geometry, representation theory, and number theory. The goals of the research school we propose are: first, to gather young researchers in order to provide them the basics on graph algebras 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 and graph C∗ -algebras; 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.

Official language of the school: English

CIMPA-2020 is addressed for researchers and students (postgraduate/undergraduate) to acquire a training in the field of mathematics applied to medicine. A wide class of mathematical models and applications in issues related to tumor growth, population dynamics, pattern formation and their implications in developmental cancer biology will be developed. Its aims are: to showcase some of the present approaches to the mathematical modeling in medicine with particular emphasis in models related to cancer; to increase the knowledge of techniques of nonlinear dynamics, Ordinary Differential Equations and numerical analysis among the participants; to foster the scientific interaction in Applied Mathematics between Cuban, Latin American and Caribbean students with the speakers from different countries; to encourage the participation of Cuban students particularly from Eastern institutions; to stimulate the participation of Cuban and Latin American and Caribbean speakers to give courses/lectures; and to stimulate the presentation (oral and/or poster) of each student.

Langue officielle de l'école : anglais

The school will provide an introduction to both basic and more advanced topics in the moderntheory of dynamical system and ergodic theory. It will be aimed mostly at Masters level students and thus assume a reasonable general mathematical background but no previous specialised knowledge in the topics covered in the courses. The scientific content of the various courses will be tightly coordinated in order to provide the students with the possibility of a real concrete learning experience which can become the foundation for further study. The material will be motivated by an overview of the field and discussion of main open problems but will consist mainly of relatively simple cases through which the students can learn specific techniques of proof. Significant amout of time will be dedicated to exercise and tutorial sessions where students will receive individual attention from the lecturers. The first week of the school will consist of three introductory courses covering the fundamental notions, definitions and the basic examples of the theory. The second week will be more advanced and include courses on random dynamical systems and extreme events, two areas which are increasingly relevant due to their connections with real world modelling of naturalphenomena.

Langue officielle de l'école : anglais

The concept of a group is central to essentially all of modern mathematics. In number theory and geometry where groups take central stage in various shapes such as symmetry groups, Galois groups, fundamental groups, reflection groups and permutation groups, the conceptual unification that it provides is most strikingly illustrated. In this school, we present groups and the natural objects they act on in a variety of arithmetic and geometric contexts. Special emphasis will be given to concrete examples, and practical and computational aspects of groups and their actions will be stressed. The topics to be treated include finite fields, coding theory covering spaces, representation theory, modular forms and Galois theory. All courses will be introductory courses.

Each course will consist of 6 lecture hours and 3 hours of training session devoted to solving exercises and to compttter assisted computations.

Langue officielle de l'école : anglais

The research school will provide a useful background to understand several of the very active research subjects in the wide area of functional analysis. This includes Riesz spaces and Stochastics processes, function theory, differential operators, operator theory on various and natural Banach spaces, some notions of geometry of Banach spaces, semigroup theory and its links with applications, without omitting an introduction to harmonic analysis. This research school will give to the students a flavour of several seminal open problems on which a wide international community of researchers is working actively. It will be useful for students who could then participate to well-known international conferences such as IWOTA (every year) or Banach Algebras (every couple of years).

Language officielle de l'école : anglais

Numeration is an active and developing field of study that encompasses different areas of mathematics and theoretical computer science. The goal of the research school is to introduce graduate students and young researchers to the fundamentals of the geometric, combinatorial, and dynamical aspects of numeration systems as well as to topics of current research. The basic courses of the research school will include lectures on beta expansions, canonical number systems, formal languages, substitutions, and others. This material is among the necessary background for other topics such as fractals and tilings arising from numeration systems (eg: Rauzy fractal), and shiftradix systems. The focus of the courses will be on the interplay between numeration systems and fractals.

Langue officielle de l'école : anglais

Since a couple of decades, Finsler geometry has been a very active field of research, with a particular stress on the use of purely metric methods in the investigation of various Finsler metrics that appear naturally in geometry, topology and convexity theory.

Our aim in this school is to provide a unified viewpoint to several aspects of this modern point of view on Finsler geometry, in the form of a set of coordinated courses that will contribute to give a solid background on this topic to the participants. The target audience will consist essentially of young researchers and PhD students from India and from developing and less developed countries, who work in this direction or who plan to pursue their research in related areas. Besides the pedagogical aspects, the interested candidates will be given directions for future research. Special attention will be given to promote female students.

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Additional information:

Training sessions.

The afternoon sessions will be exclusively dedicated to tutorials and discussions. The coordinators of the training sessions and complimentary lecturers will include:

• Muhammed Uludag (Galatasaray University)
• Norbert A’Campo (Univ. Basel)

The Escuela Latinoamericana de Geometría Algebraica (ELGA) series of schools quickly became a major event for algebraic geometry in Latin America working as meeting point for the whole community due in part to the novelty of having some of the best researchers in our eld lecturing in Latin Americaf

The goal of this Fourth Edition is again to bring experts in algebraic geometry and present diferent topics of current research to advance graduate students, postdocs and young researchers from Latin America and other parts of the worldf There will be ve main courses and several survey lectures in english on a wide range of themes in algebraic geometry and its applications, completed by a series of research talks given by young researchersf

The main courses will be given by : Jean-Pierre Demailly, Igor Dolgachev, Angela Ortega, Vincent Pilloni and Claire Voisinf 

The classical results and open problems that lie at the interface between commutative algebra and algebraic geometry, have undergone a striking evolution over the last quarter of a century, aided in large part by computer algebra calculations. At the heart of all these developments is the concept of syzygies: the analysis of the algebraic relations (syzygies) between the equations defining a geometric object leads to deep insights of its geometric properties. The aim of this CIMPA research school is precisely to introduce graduate students and young researchers to some fundamental techniques and recent developments on syzygy-based methods, including their application to combinatorial and toric geometry, module of differentials, the Minimal Resolution Conjecture, regularity of powers of ideals, geometric properties of rational maps and geometric modeling. Besides the six courses, computational and problem solving sessions are planned in order to train the students to the use of free computer algebra systems.