Turkey

The 2007 Summer School will consist of two sections, Arrangements & Local Systems and Singularities. Historically these two fields are closely related, require the same mathematical background and often similar tools are employed in their study. The aim of the ALS Summer School is to give its students a working knowledge on local system cohomology.

The summer school will be followed by a workshop on Hyperplane arrangements.

The aim of the school is the presentation of hot topics in the field in a form accessible to research students, and revival of the interest in the field by highlighting possible new research directions. There will be minicourses on hypergeometric differential equations and related topics such as discrete groups in the automorphism groups of complex balls, ball quotients, orbifolds and corresponding moduli problems of algebraic geometry. Quotient of a ball under a discrete group action is called a ball-quotient.

There is already a fairly large community of mathematicians specializing in commutative algebra in Turkey. The general consensus of this community is that the interaction with related areas of algebraic and arithmetic geometry and combinatorics will enhance the vitality of the research in this field. A primary goal of the school is to cultivate such interaction.

From the seminal work of Shannon of 1948 till the end of the 80's the algebraic framework of the theory of error correcting codes was within the confines of vector spaces over finite fields. Beginning in the early nineties a paradigm shift occurred , and modules over finite rings entered the armory of coding theorists from engineering applications like low correlation sequences to finite geometry and number theory .
The aim of this school is to present a survey in fundamental areas, and to host a mini-conference highlighting some recent results.

This is a two-week long research summer school on algebraic geometry and related number theory. Topics to be included are Computational commutative algebra, Subvarieties of low degree in projective spaces, sheaf cohomology, Singular points of complex hypersurfaces, Birational geometry of moduli spaces, Arakelov theory and Hypergeometric Galois actions. We plan to deliver a series of preparatory lectures before the summer school. There will be a possibility for young researchers to present short research talks and make poster presentations.

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.

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.

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 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 .

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 .

The summer school aims to gather young researchers and to give a motivating goal along which the participants will be able to aggregate new knowledge. The research topics include function field arithmetic, algebraic curves over finite fields, complex multiplication, boolean functions, finite geometry, and combinatorics. The school will be mostly structured into working sessions in small groups under the direction of at least one lecturer. Before the beginning of the school, the lecturers will propose open problems together with pre-request material (books/papers).