2015

Number theory is both one of the core areas of mathematics and a crossroads for many other disciplines. Analysis, diophantine geometry and combinatorics, among other areas, have a long history of interaction with number theory ; other subjects, such as group theory and ergodic theory, are also developing often surprising connections with the field.

This will be a two-week school, following the lead of the first AGRA meeting in Santiago, Chile, 2012. The main aim of the series is the development of number theory (in the broadest sense) as an area of research in South America.

Stochastic Processes and Applications Mongolia 2015 will be hosted by the School of Mathematics and Computer Science at the National University of Mongolia. Situated in the capital city Ulan Bator, this event takes place at the very heart of Asia and is open to all. The two-week research school will look at classical and contemporary topics from the theory of stochastic analysis with applications.

Realising the need to demonstrate application of dynamical systems in real life situations and to expose the participants to mathematical skills of formulating complex dynamical models for biological and technical systems gave birth to this school. The need motivated our desire to give our postgraduate students skills in mathematical modelling and analysis of complex dynamic models.

Representation Theory of Lie algebras and Group Theory will be the topics of the Research School Algebraic Representation Theory 2015.

Recent research trends including:

Numerical analysis, simulation and scientific computing for the solution of partial differential equations (PDEs) using FEM and related methods have been cornerstones of applied mathematics over the last fifty years. In fact, it is well known that the study of computational methods for PDEs is extremely crucial for the development of science and technology.

Point processes are well studied objects in probability theory, with applications in many different disciplines such as nuclear physics, materials science, telecommunications, astronomy, artificial intelligence (machine learning) and economics, among others. Some interesting point processes can be obtained as eigenvalues of random matrices or as zeros of series expansions with random coefficients.

Graphs are combinatorial objects that sit at the core of mathematical intuition. They appear in numerous situations all throughout Mathematics and have often constituted a source of inspiration for researchers. A striking instance of this can be found within the classes of graph C*-algebras and of Leavitt path algebras. These are classes of algebras over fields that emanate from different sources in the history yet quite possibly have a common future.

The goal of this CIMPA research school is to train young mathematicians working in Latin America in some of the most active areas of research in Algebraic Geometry, as well as to promote greater interaction among researchers and students, and to build a network of collaborations.

The first week of the school will consist of 4 mini-courses covering different aspects of Algebraic Geometry. There will be also poster presentations by young researchers and students. The second week will consist of research talks by leading specialists, as well as presentations by young researchers.

Many problems in mathematics concern with classification once a notion of equivalence is given in a class of mathematical objects. Classically, the theory of invariants proposes to study the orbits of a group action over a geometric object and the properties which remain stable under this action.
The aim of this CIMPA school is to give an introduction to different techniques in this context related with the study of holomorphic foliations and differential equations from a local and global viewpoint. More precisely, the courses will cover the following subjects:

The goal of this school is to introduce the students to basic questions and methods in dynamical systems through concrete examples. Our basic questions are: Existence of cloded orbits, integrability (ie, complete solvability), and stability. And the methods are: geometrization and variational principles. We shall do this by illustrating these questions and methods by elementary and archetypical examples of dynamical systems: Billiards, geodesic and magnetic flows, and the 3-body problem.