2017

La géométrie non commutative (GNC) est une sujet de recherches très actif en mathématique et en physique. Le but de cette école est de former des étudiants et des chercheurs locaux dans ce domaine et d’établir des collaborations.

The scope of problems accessible for a numerical treatment has been constantly broadened over the last fifty years. In particular, there has been a lot of research activity in the recent decades aimed at the problems with multi-scale and multi-physics features. The dedicated numerical methods (model reduction, micro-macro models and model coupling, non standard FEM) stem from diverse techniques and ideas such as homogenization, asymptotic analysis, statistical physics, domain decomposition methods, etc.

This research school intends to present to the participants (mainly Ph.D. students) applications of commutative and non-commutative algebra to coding theory. Thus we will have courses and talks on the following topics (but not limited to them):

Recent developments in non-commutative algebra include parallel theories of graph C*-algebras and Leavitt path algebras. In this research school, we mainly focus on theories of Leavitt path algebras and their connections with other areas of mathematics.

This research school will introduce the participants to some basics of algebraic geometry with an emphasis on computational aspects, such as Groebner bases and combinatorial aspects, such as toric varieties and tropical geometry. We will also learn how to use the freely available software Macaulay2 for studying algebraic varieties. The lecturers for this school are all active in these areas and collectively have deep experience both as researchers and educators through the supervision of students ; Ph.D. and postdoctoral, as well as the organization of and lecturing in short courses.

This school is intended to foster anlytic number theory as well as algebraic number theory and arithmetic geometry in Turkey. The school revolves around Artin’s primitive root conjectures and Artin’s L-functions, two subjects that lie at the crossroads of these three fields.

L’école vise deux objectifs majeurs :

La liberté, dans sa acception probabiliste, est une forme d’indépendance adaptée à des variables aléatoires non commutatives. Elle a été introduite par D. V. Voiculescu dans le but de résoudre le problème de Kadison sur l’isomorphisme entre les facteurs de von Neumann du groupe libre. La théorie des probabilités libres qui en est issue présente beaucoup d’analogies avec les probabilités classiques tout en ayant des outils et des champs d’application distincts.

Algebraic number theory is a very active field of mathematics. We plan to introduce the subject and its application to cryptography. After given courses in elementary arithmetic, algebraic numbers and p-adic numbers, we will focus on the basics of elliptic curves and finite fields. Applications will also figure prominently in the program as it is shown by the presence of the following courses : Introduction to cryptography, Elliptic curves and cryptography.

L’école de recherche « Spatial Statistics : Extreme Value and Epidemiology » est destinée à présenter les aspects théoriques de la statistique spatiale et de ses applications aux valeurs extrêmes et à l’épidémiologie.

Cette école est destinée à des étudiants en dernière année de master, des doctorants, des enseignants chercheurs et des praticiens non spécialistes, ayant un bon bagage en statistique et qui souhaitent orienter leurs recherches vers la statistique spatiale et plus spécialement les extrêmes spatiaux et l’épidémiologie spatiale.