English

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):

• The broad use of techniques from finite group algebras to study, among others, cyclic, abelian and metacyclic codes;
• Evaluation codes constructed from ideals in polynomial rings;
• Applications of Gröbner basis methods to the estimation or computing of code parameters and decoding;
• Applications of results from Hilbert functions and regularity of ideals to the estimation or computing of code parameters;
• Convolutional codes;
• Applications of numerical semigoups theory to coding theory;
• Codes over rings.

The main motivation of this school is to introduce students to coding theory as an area of research. We expect students firstly to understand the basics of coding theory, and then to get a working knowledge of some methods coming from both commutative and non-commutative algebra which are currently being applied successfully to study a variety of codes. Our aim is to prepare students to pursue research in this area, by using the tools described in the short courses and talks. A second motivation for this school is to promote the exchange of experiences among researchers and students from different parts of the country and from abroad.

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.

Leavitt path algebras arose out of the work of Leavitt (1962) and the graph C*-algebras trace their origin to the work of Cuntz (1977). These algebras were introduced about ten years ago by Abrams – Aranda Pino, and Ara – Moreno – Pardo in two separate papers. It is an algebraic analogue of C*-algebras, a subject which originated in the late 1990s in the work of Kumjian – Pask – Raeburn – Renault, and has been pioneered by the Australian researchers, including Bates, an Huef, Pask, Raeburn, Sims, Szymanski et.al.

Although the two areas — Leavitt path algebras and graph C*-algebras — sprang from independent works, they are closely related. There are many striking parallels between the two subjects, and many of the key results first arising in either one of the two fields turn out to have an exact analogue in the other. In terms of research, the main goal of the school is to explore K-theoretic techniques, and the graded structures of both the Leavitt path algebras and the graph C* algebras as tools for understanding the similarities and the differences between the two areas.

Apart from the above mentioned topics, we will also discuss some recent developments in the direction of homological algebra and deformation theory. Algebraic deformation theory is primarily concerned with the interplay between homological algebra and the perturbations of algebraic structures. On hopes to explore some future developments of the theory of Leavitt path algebras in this direction.

There will be some introductory courses on Lie algebras, Basic K-theory and graph C*-algebras. One each day of the research school there will be some tutorial sessions for the beginners.

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. It will give the attendees the opportunity to learn some basics notions on the following topics: a brief introduction to algebraic number theory culminating in the celebrated Chebotarev Density Theorem; an introduction to the representation theory of finite groups culminating in the definition of Artin’s L-functions and the group theoretic proof of their meromorphicity; an introduction to zeta functions and L-functions; distribution of primes; an introduction to elliptic curves and analogues of Artin’s Conjecture, and last but not least Hooley’s Theorem and quasi resolution. All courses will be taught in English.

The research school " Spatial Statistics : Extreme Value and Epidemiology " is intended to present the theory of spatial statistics and its applications to extreme values ​​and epidemiology .

This school is suited for students, PhD students, researchers and non-specialist practitioners, having a good background in statistics, who want to direct their research on spatial statistics in particular spatial extremes and spatial epidemiology.

The courses will focus on the foundations of spatial statistics and their applications:

• Geostatistics and spatial statistics on lattice.
• Univariate, multivariate and spatial Extreme value theory.
• Epidemiology and food risk.

The CIMPA research school "Representation Theory and Applications to Differential Equations" is intended for PhD and postdoctoral students from Jamaica and surrounding Caribbean and American countries and specifically for students in the region. The CIMPA research school “Representation Theory and Applications to Differential Equations" offers courses and research talks on advanced research topics related to the representation theory of groups and algebras, related differential equations and other topics. The school lasts two weeks, featuring 6 courses and 12 research talks.

The topics of the school include Representation Theory of groups and algebras and their applications to Differential Equations, including integral representations, integral group rings, Vertex algebras, algebras of differential operators, representations of Krichever-Novikov algebras, Hilbert series of Calabi-Yau algebras, differential conformal superalgebras, soliton theory for Korteveg-de-Vries Equation, Heun functions and applications in the physics of black holes.

In this school, we will introduce differential equations as modeling tools in engineering (fluid dynamics, traffic flow) and bio-mathematical applications (coagulation, epidemics). We will discuss analytical properties of differential equations and their numerical solution.

The aim is to provide the basic tools that will allow the students to proceed to more theoretical subjects or venture into more concrete applications. Theoretical and numerical lectures will be given, with a particular attention being paid to numerical simulations using free scientific computing softwares such as Scilab or Python.

The school will be composed of three main components: The first one will consist in lecture-series, the second component will be a series of advanced talks involving internationally confirmed researchers, while the third pedagogical tool of the Cimpa school will be a program of mini-projects built around topics covered in the school. These projects will concentrate on constructing basic numerical solvers for specific applied problems.

Mathematical modeling in biology and medicine is undergoing a major development in order to meet the health and environmental challenges we face today. It allows better understanding, and accurate prediction of the dynamics of complex biological systems. Specific tools based on ordinary or partial differential equations and optimization methods need to be developed in collaboration with Mauritius, Réunion, Malagasy Republic, South Africa and other countries of the Indian Ocean, particularly with respect to the epidemiological aspects. The main aim of the school is to present and discuss the related mathematical principles and the recent developments and advances in mathematical medicine and biology. It will be an opportunity for postgraduate students and researchers to gain a basic training in the latter area. The school aims to cover a broad spectrum of mathematical modeling in biology and medicine, with an emphasis on population dynamics, epidemiology, and hemodynamics mainly. It will include sessions on both the theoretical analysis of partial differential equations and on their numerical discretization.

Geometric flows are burning topic now a days which involve the evolution of Riemannian metric along with some geometric concepts.

In this research school we shall discuss about evolution of Riemannian metric with respect to time. Ricci flow, mean curvature flow and some type of other Geometric flow will be studied thoroughly. The main objective of this course will be to study the singularity formation in the case of Mean Curvature Flow and Ricci Flow. The concept of Ricci soliton was introduced by R. Hamilton in mid 80’s and they are self-similar solutions to Hamilton’s Ricci flows. The Ricci solitons and gradient Ricci solitons will also be studied. The discussions about Ricci Solitons as Contact Riemannian Metrics also be done.

We want to motivate researcher of our country and our neighbouring countries in this field, so that they can apply it in the various field of Physics and Mathematics. The aim of the Research School is to provide students with the basic as well as more advanced notions of both theories and applications.

The objective of our school is to introduce participants to the formulation of mathematical and computer models in epidemiology, immunology, ecology and agronomy and the use of tools of dynamical systems and numerical analysis in the analysis of real situations epidemics within a human or animal population of pests of plants and plant population dynamics.