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Our goal is to organize a conference devoted to interactions between pure mathematics, in particular arithmetic and algebraic geometry, and the information theory, especially cryptography and coding theory. This conference will be the seventeenth edition, with the first one held in 1987, that traditionally reunites some of the best specialists in the domains of arithmetic, geometry and information theory. The corresponding international community is very active with all of the concerned domains changing rapidly over time.
The conference is thus an important occasion for young mathematicians (graduate students and post-docs) to interact with established researchers in order to exchange new ideas.
The conference talks will be devoted to recent advances in arithmetic and algebraic geometry, and number theory, with a special accent on algorithmic and effective results and applications of these fields to the information theory.
The conference will last one week and will be organized as follows :
- One or two plenary talks per day at the beginning of each session. They will be given by established researchers, some of them new to the established AGC2T community, so that that new emerging topics can be introduced, that may give rise to new applications of arithmetic or algebraic geometry to the information theory.
- Shorter specialized talks, often delivered by young mathematicians.
As with the previous editions of the AGC2T, we would like to publish the acts of the conference as a special volume of the Contemporary Mathematics collection of the AMS.
- Number theory, asymptotic properties of families of global fields, arithmetic statistics, L-functions.
- Arithmetic geometry, algebraic curves over finite fields or number fields, abelian varieties : point counting, the invariant theory and classification of curves.
- Coding theory, algebraic-geometric codes constructed from curves and higher dimensional varieties, decoding algorithms. - Cryptography, elliptic curves and abelian varieties : the discrete logarithm problem, pairings, explicit computation of isogenies, multiplication over finite fields, APN functions, bent and hyper-bent funtions.
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