Mexico

This school is an introduction to subjects of current interest related to vector bundles. The aim of the courses is to provide the necessary tools for conducting research in these areas. Each course will start with classical material and will take the audience to the frontier of research in the subject. Considering the wide range of topics that to be covered, the School will be directed at students and researchers in mathematics and physics interested in the subject. One of the aims of the school is to promote interaction between the participants and the experts.

This school is an introduction to different subjects related with the propagation of waves. Considering that waves occur in nearly all branches of physics and engineering, with the general title "Propagation of waves'' we can integrate several topics of interest in the region. The course can integrate pure and applied mathematicians, physicists and engineers in a wide topic that includes some of the most relevant areas in the region such as seismic waves or oil recovery.

The three domains are related and have common applications (for example error correcting codes, cryptography). We will develop these topics not only from a theoretical or applied point of view, but also by pointing out the algorithmic aspects and by connecting them with formal computation. This school is intended for introducing young researchers to this main area. For those currently working in this domain, it is a good opportunity to complete their knowledge on particular points.

The school has as its main objective to provide different perspectives on singularity theory. These (usually complementary) include the theory of Poincaré­Hopf and characteristic classes, commutative algebra, real and complex algebraic geometry, holomorphic foliations and tropical geometry among others.

The goal is that students and young researchers increase and enrich their knowledge about several aspects of the theory of singularities, and have contact with experts on the subject.

The aim of this school is to introduce graduate students and postdoctoral researchers to contemporary developments in the theory of Associative and Nonassociative Algebras and Dialgebras.

Algebraic geometry is a key area of mathematical research of international significance. The Theory of Moduli Spaces has experienced an extraordinary development in recent decades, finding an increasing number of mathematical connections with other fields of mathematics and physics. This school is an introduction to subjects of current interest related to moduli spaces of augmented bundles and physics.

The ASReCoM aim is to fill in the gap between the theoretical part of
algebraic geometry and the applications to problem solving and computational
modeling in engineering in signal processing and information theory which
involve non trivial knowledge of algebra and geometry. The students of this
school will receive both theoretical and practical insight in those topics and
as it is traditional on modeling schools also in the software needed for
dealing with those modeling problems.

This school is an introduction to subjects of current interest related to moduli, a fundamental aspect of algebraic geometry, with emphasis on moduli of curves. The propose of this school is to introduce young mathematicians to the foundations of the theory, some of its major developments and tools used for its study and also a few glimpses on some more advanced topics. Each course will start with classical material and will take the audience to the frontier of research in the subject.

The autumn school will show recent developments in index theory in connection with noncomuutative geometry and global analysis. The scientific programme will include topics related to Secondary index theory, index theory for manifolds with singularities, Lie groupoid’s techniques in index theory and methods from topological K-Theory and noncommutative geometry.

Commutative algebra and its multiple applications have grown considerably in recent years. The main purpose of the school is to present both, basic aspects of commutative algebra as well as more advanced tools focused on applications to combinatorics, coding theory and statistics. Participants will be provided with the basics on the combinatorics of binomial ideals and its relations with coding theory and algebraic statistics problems through courses and talks on the following topics: