English

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

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.

Official language of the school: English

The summer school will be dedicated to finite point configurations and rigidity, Erdos problems in discrete geometry and frame theory, the Falconer distance conjecture  in  geometric  measure  theory,  discrete  integrable  systems  and connections between these topics.  Participants will  be introduced to various open problems and possible research projects  in these very active research areas.

Official language of the school: English

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  q-series)  and  techniques  (various  enumeration techniques  and  analytic  methods  such  as  singularity  analysis).  The more advanced courses  will  build on these and discuss  various  more specialised topics,  related to  random graphs  and trees,  automata  and the  analysis  of algorithms. These  topics  are  connected  in  various  ways,  not  only methodologically.

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.

Official language of the school: English

This school, whose topics lie at the threshold of geometry, topology, algebra and quantum field theory, is the eleventh of a series of summer schools organised in Colombia every other year since July 1999. It is addressed to both physicists and mathematicians with a master’s level in either of the fields and offers courses on the following topics:

• Fully extended topological field theories by D. Calaque,
• Ruelle and quantum resonances by C. Guillarmou
• Double Field Theory by C. Nuñez
• Mathematical aspects of perturbative quantum field theory by K. Rejzner
• Random Matrices and Tensors by V. Rivasseau
• Topological Finite Group Gauge Theories by P. Putrov.

Additional introductory courses will be offered, that are meant to fill in specific knowledge gaps for students of one discipline mathematics or physics, in the other discipline.

Official language of the school: English (and occasionally Spanish)

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.

Official language of the school: English

This School aims to bring together graduate students and young researchers from all  regions in Brazil and countries of the South America as audience, and confirmed researchers from all over the world representing different approaches to singularities in Mathematics as speakers.

The school will offer a solid introduction to this rich topic  by presenting the fundamentals of the topology and geometry of singularities of spaces and maps, and of the geometric bifurcation theory, together with the necessary algebraic and analytic tools, aiming to a bunch of current research lines.
Will be presented ongoing research topics such as determinantal varieties, bifurcation of families, fibrations structures and new classes of singularities, Lipschitz geometry of singularities, vision and other applications. All courses will be planned to provide the students with practical tools via the open source computer algebra system ‘Singular’.

Official language of the school:  English

IMPORTANT:

This school will take place in two stages: a first online part in 2021, then a second face-to-face part in 2022.

One of the fascinating bridges between  classical  mechanics  and quantum physics  is expressed  in the fact that the length spectrum  and the Laplace  spectrum  of a closed Riemannian  manifold determine  each other (at least generically). The main goal of this school  is to introduce  graduate  students  and young  researchers to basic facts on these two spectra, and to the above correspondence.

The length spectrum  generalizes   to the action spectrum  of an autonomous Hamiltonian function.  Floer homofogy filtered  by the action spectrum  can be used to construct  so-called  action selectors,  that are a principal  tool in modern symplectic  geometry and dynamics.

The second goal is to understand  this relevance  of the action spectrum  in symplectic geometry.

A third,  more hypothetical, goal is to see which parts  of the two sides can be related.

Official language of the school: 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.

Official language of the school: English