Its recent triennial congresses, held in association with the business meetings of the Union General Assemblies are attended by 2, to 3, scientists.

## Mathematical crystallography and the theory of groups of movements

The Union also organizes or sponsors many smaller meetings. It has formed 18 Commissions, which are concerned with either a principal publishing activity or a major topic or field of concern to crystallographers.

The second group of Commissions organize many international projects concerned with the establishment of internationally acceptable standards or methods of procedure. Also, they organize specialist meetings or short courses of instruction for young scientists. The Union publishes its own international scientific journal, Acta Crystallographica, the major journal for publication of crystallographic research.

Today it runs to 8, pages a year and is divided into five sections. The fifth section, Structure Reports Online, is an electronic-only journal, launched in January Number theory and arithmetic geometry: elliptic curves and the Birch and Swinnerton-Dyer conjecture, Euler systems and Selmer groups, special cycles on Shimura varieties; mathematical foundations of cryptology and applied cryptography: curve-based cryptography, complexity of computing discrete logarithms, hard-to-compute bits, secure multiparty computation and applications.

Analytic Number Theory, Analytic properties of Automorphic forms and their representations, Ergodic theory on arithmetic homogeneous spaces.

Pure Mathematics. The main focus of the Chair of Algebraic Geometry is the classification theory of higher-dimensional algebraic varieties, including exploring its connections to adjacent fields such as commutative algebra, arithmetic geometry and complex geometry.

Amin Shokrollahi Mohammad. He is best known for his work on iterative decoding algorithms of graph-based codes.

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- Dreaming in Code: Two Dozen Programmers, Three Years, 4,732 Bugs, and One Quest for Transcendent Software.