2018

In this school, we will discuss 6 different themes from Combinatorial Commutative Algebra. The idea of Combinatorial Commutative Algebra is to relate combinatorial objects, like simplicial complexes, graphs, hypergraphs or polytopes to algebraic objects like monomial, binomomial ideals and toric rings. The field benefits from the interplay between properties of combinatorial objects and the corresponding properties of the algebraic object. The binomial edge ideals as well as edge ideals of graphs and their powers as well as their symbolic powers will be considered.

This school is an introduction to subjects of algebraic coding theory and quasi cyclic codes. The purpose of this school is to introduce young mathematicians and students to the foundations of the study of error correcting codes by means of algebra over finite rings and finite fields. Powerful decoding algorithms and connections with geometric codes will be emphasized when relevant. Applications to convolutional codes will be presented .

Interactions between analysis and geometry are of considerable importance in mathematics. The famous Yamabe problem and Perelman’s proof of Poincaré are remarkable illustrations of these interactions. The aim of this school is to provide an introduction to some of these topics, focusing on geometric problems that are expressed in terms of elliptic equations.

Many classical results and methods of Number Theory are now actively used in important domains of applied mathematics like Cryptography,CodingTheory or Numerical Analysis.To enable these applications one must have explicit versions of these number-theoretical results and tools. This is why Explicit Number Theory emerged and rapidly developed during the last several decades.

In this CIMPA school we plan to introduce the students to this field. The following list is a sample of the topics that will be considered: